05. Mathématiques/05. Equations différentielles/01. Equations differentielles en python.ipynb

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    "# Introduction aux Equations différentielles en python\n",
    "\n",
    "\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/intro.jpg\">\n",
    "</div>\n",
    "\n",
    "\n",
    "## Introduction\n",
    "\n",
    "Une équation différentielle permet de décrire et analyser un système dynamique, autrement dit, un système en mouvement.\n",
    "\n",
    "Dans les premiers cas pratiques étudiés, le temps est gradué sur l'axe des abscisses, et l'on étudie un évènement qui se déroule dans le temps. Une équation différentielle est une équation dont la solution est une, ou parfois plusieurs fonctions.<br><br>\n",
    "Dans les cas complexes, pour les robots, la notion d'angle intervient en fonction du temps, ce qui compliquera forcément les notations, de plus, cela implique des systèmes d'équations différentielles puisque que la base tourne, mais aussi le bras, la pince, et bien sur, tout cela \"bouge\" en même temps, on fera donc une introduction à la cinématique en fin de notebook ...<br><br>\n",
    "Dans ce notebook, je pars de la base de chez base du Lycée, pour que ce soit facile au début, puis on incrémente la difficulté au fil du notebook.</br>On se sert de Python pour automatiser au maximum les calculs, et pouvoir aller plus vite, et attention, dans ce notebook, on compare toujours les résultats aux sources citées, pour confirmer que la solution soit exacte. Le but final étant d'être opérationnel sur des cas pratiques de base impliquant des équations différentielles.<br>\n",
    "\n",
    "\n",
    "<b>Notebook réalisé par Github Estelle Derrien</b>\n",
    "\n",
    "** En cours de création / Sujet quelques erreurs au début ! Je croise de nombreuses sources en Français et en Anglais pour réaliser ce notebook**\n",
    "\n",
    "## Rappels\n",
    "\n",
    "- y est une fonction, cela équivaut à f(x) au Lycée.\n",
    "\n",
    "- <b>y'</b> est la notation de la dérivée de la fonction y au format <b>Lagrange</b>.\n",
    "\n",
    "$$\\frac{dT}{dt}$$\n",
    "\n",
    "-  <b>dT/dt</b> est un exemple de la notation de la dérivée au format <b>Leibniz</b>, soit T la température,alors, cela veut dire  \"<b>Evolution de la température T en fonction du temps t</b>\" ( C'est la notation en sciences physique, et remarquer l'importance de l'indentation). Autre exemple, <b>dC/dt</b> : soit C le capital, alors cela veut dire \" <b>Evolution du capital C en fonction du temps t\"</b>\n",
    "\n",
    "- Une équation différentielle d'ordre un comprends une dérivée première (notée y'), une équation différentielle d'ordre deux comprends une dérivée seconde (notée y'')\n",
    "\n",
    "- Au début, on étudie des phénomènes <b>en fonction du temps</b>, mais après cela pour être <b> en fonction d'autre chose</b>, par exemple , l'évolution de la quantité de bactéries en fonction de la densité d'un corps gazeux, ou toute autre joyeuseté, on verra des exemples là dessus aussi.\n",
    "\n",
    "- Les lettres ne sont pas réservées, par exemple, un taux sera noté k dans une équation différentielle, mais r dans une autre.\n",
    "A titre personnel, j'aime quand une nomenclature récapitulative est écrite en dessous de l'équation différentielle, mais sinon, il faut la reconstituer mentalement. En recherche opérationnelle, on place toujours une nomenclature en dessous du modèle.\n",
    "\n",
    "## Liens \n",
    "Excellent liens en Anglais :\n",
    "- https://quantdev.ssri.psu.edu/sites/qdev/files/ODEintro_tutorial.html\n",
    "\n",
    "- https://personal.math.ubc.ca/~CLP/CLP1/clp_1_dc/sec_ExpGthDecay.html\n",
    "\n",
    "Lien plus difficile ,Cpge :  \n",
    "- https://cpge.frama.io/fiches-cpge/Python/%C3%89quation%20diff%C3%A9rentielle/0-Equation%20diff%C3%A9rentielle/#exemple-systeme-masseressort\n",
    "- https://physique.merici.ca/calcul/chap6cal.pdf\n",
    "\n",
    "## Sommaire:\n",
    "\n",
    "\n",
    "- <b>Introduction.</b>\n",
    "\n",
    "1. <b><span style=\"color:green\">Résoudre une équation différentielle d'ordre 1 ->  y' = ax</span></b> \n",
    "\n",
    "    - <b>y' = 2x</b>\n",
    "        - Solution Logique\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "        - Solution Algébrique avec dsolve\n",
    "        - Annexe : Comparaison avec les suites géométriques\n",
    "\n",
    "2. <b><span style=\"color:green\">Résoudre une équation différentielle d'ordre 1 sans second membre -> y' = ay</span></b> \n",
    "    \n",
    "\n",
    "    - <b>y' = 2y</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "        - Solution Algébrique avec DSolve\n",
    "\n",
    "    -  <b>5y’ + 2y = 0</b>\n",
    "        - Solution Symbolique\n",
    "            - Déterminer la solution générale de cette équation avec Sympy\n",
    "            - Déterminer l’unique solution de l’équation telle que y(1) = 3 avec Sympy\n",
    "\n",
    "    - <b>3y' + 5y = 0</b>\n",
    "        - Solution Symbolique\n",
    "            - Déterminer la solution générale de cette équation avec Sympy\n",
    "            - Déterminer l’unique solution de l’équation telle que 𝑓(1) = 2 avec Sympy\n",
    "    - <b>dy/dt = -yt + 13</b>\n",
    "        - Solution Symbolique\n",
    "            - Déterminer la solution générale de cette équation avec Sympy\n",
    "    - <b>Le problème de Chauchy</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "\n",
    "    - <b>Des sin et des cos</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique \n",
    "\n",
    "    - <b>Cas pratique 1 : Croissance constante linéaire</b>\n",
    "        - Graphiquement.\n",
    "        - Solution Symbolique\n",
    "\n",
    "    - <b>Cas pratique 2 : Croissance exponentielle</b>\n",
    "        - Exemple des lapins\n",
    "        - Résoudre Graphiquement.\n",
    "        - Solution Symbolique.\n",
    "        - Exemple 2.1 :  Croissance de bactéries et interpolation pour résultat numérique exact\n",
    "        - Exemple 2.2 : Solution chimique  et temps exact avant de trouver un résultat précis\n",
    "        - Exemple 2.3 : Tracer plusieurs eq diffs avec un différent taux k pour comparer.\n",
    "        - Croissance de population logistique ( Ressources limitées)\n",
    "        - Croissance de population avec prédation\n",
    "\n",
    "    - <b>Cas pratique 3 : Loi de réchauffement / refroidissement de Newton</b>\n",
    "        - Exemple 1 : Température d'un thé en fonction du temps\n",
    "            - Solution Graphique\n",
    "            - Solution Symbolique\n",
    "        - Exemple 2 : Température du corps en fonction du temps (Santé/cadavre enquête police)\n",
    "            - Solution Graphique\n",
    "            - Solution Symbolique\n",
    "\n",
    "    - <b>Cas pratique 4 : Finances - L'évolution d'un avoir placé à intérêts composés à taux fixe.</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "    \n",
    "\n",
    "        \n",
    "    - <b>Cas pratique 6 : Taux de salinité en reservoir percé</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "\n",
    "\n",
    "\n",
    "3. <span style=\"color:green\"><b>Résoudre une équation différentielle d'ordre 1 avec second membre <b>constant</b> -> y' = ax + b </b></span>\n",
    "\n",
    "    - <b>Cas pratique : Température d'une tarte en fonction du temps </b>\n",
    "        - Description\n",
    "        - Entrer l'équation différentielle dans SYMPY\n",
    "        - Trouver la solution générale\n",
    "        - Trouver la fonction de la température en fonction du temps grâce à t(0).\n",
    "        - Calculer la température de ma tarte après 30 minutes.\n",
    "\n",
    "    - <b>Cas pratique 2 : Charge et décharge d'un condensateur </b>\n",
    "        - https://www.youtube.com/watch?v=zV4pOe7g260\n",
    "        - Description\n",
    "        - Entrer l'équation différentielle dans SYMPY\n",
    "        - Trouver la solution générale\n",
    "        - Trouver la fonction de la charge en fonction du temps grâce à t(0).\n",
    "        - Calculer la charge de mon condensateur après 10 minutes.\n",
    "        - Exemple de code avec affichage de la charge et la décharge simultanée.https://stackoverflow.com/questions/65470318/calculating-charging-discharging-curves-of-a-rc-circuit-by-integration\n",
    "        - https://web.enib.fr/~kerhoas/equa_diff.html\n",
    "        - http://physapp.giraud.free.fr/tgel/astable/chargec.htm\n",
    "4. <span style=\"color:green\"><b>Résoudre une équation différentielle d'ordre 1 avec second membre <b>variable</b> -> y' = ax + x² </b></span>\n",
    "\n",
    "    - <b>Cas Pratique </b>\n",
    "        - Description\n",
    "        - Solution Symbolique \n",
    "        - Solution Graphique \n",
    "5. <span style=\"color:green\"><b>Résoudre une équation différentielle d'ordre 1 avec second membre <b>fonction</b> -> y' = ax + f(x) </b></span>\n",
    "\n",
    "    - <b>Cas Pratique </b>\n",
    "        - Description\n",
    "        - Solution Symbolique \n",
    "        - Solution Graphique\n",
    "\n",
    "6. <span style=\"color:green\"><b>Résoudre un système d'équations différentielles d'ordre 1</b></span>\n",
    "\n",
    "    - <b>Exemple </b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "\n",
    "\n",
    "7. <span style=\"color:green\"><b>Résoudre une équation différentielle d'ordre 2 -> y'' ...</b></span>\n",
    "\n",
    "    - <b>Cas pratique : Vitesse et accéleration</b>\n",
    "        - Solution Graphique\n",
    "        - Solution Symbolique\n",
    "\n",
    "8. <span style=\"color:green\"><b>Modéliser une équation différentielle de robot manipulateur</b></span>\n",
    "\n",
    "    - <b>Cas Pratique </b>\n",
    "        - Description\n",
    "        - Solution Symbolique \n",
    "        - Solution Graphique  \n",
    "\n",
    "9. <span style=\"color:green\"><b>Annexes</b></span>\n",
    "    - Annexe : Comparaison eq diff ordre 1 avec les suites géométriques   \n",
    "\n"
   ]
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   "source": [
    "# <span style=\"color:green\"> <b>1. Résoudre une équation diff d'ordre 1 -> y' = ax</b> </span>\n",
    "-------------------------------------------------------------------------------------------------------"
   ]
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    "\n",
    "## <strong>L'équation différentielle<span style=\"color:red\"> y'=2x<span></strong>\n",
    "\n",
    "\n",
    "Ici, y' est une <b>dérivée</b> , 2 est une <b>constante</b>, x est une <b>variable</b>, .\n",
    "\n",
    "\" On a une fonction dont la dérivée est égale à 2 fois la variable x\"\n",
    "\n",
    "\" L’inconnue est la fonction 𝑦 dont la dérivée est égale à 2x \" \n",
    "\n",
    "Lien : https://www.youtube.com/watch?v=qHF5kiDFkW8\n",
    "\n",
    "\n",
    "\n"
   ]
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",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"800\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/qHF5kiDFkW8\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x240494d48b0>"
      ]
     },
     "execution_count": 2027,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('qHF5kiDFkW8', width=800, height=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <b>Solution Logique.</b>\n",
    "\n",
    "Grâce au tableau des dérivées usuelles du Lycée, on sait que la fonction x² a pour dérivée 2x.<br>\n",
    "Par déduction, la fonction qui est solution de l'équation différentielle est donc x²"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <b>Solution Graphique </b>\n",
    "\n",
    "On cherche la solution graphique de notre équation différentielle. La solution étant une fonction ,ça dessine une fonction, la fonction f(x) = x² . C'est grâce à ces dérivées successives que l'on reconstitue et dessine f(x) = x² sur l'intervalle [0;10]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2028,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import des libs\n",
    "from scipy import *\n",
    "from scipy.integrate import odeint #Pour résoudre l’équation différentielle\n",
    "import matplotlib.pyplot as plt # Permet de tracer des graphes\n",
    "import numpy as np\n",
    "from math import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2029,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Au temps 10, ma valeur sera de  101.000000001241\n"
     ]
    }
   ],
   "source": [
    "# fonction qui retourne la dérivée pour chaque x fourni à la fonction np.linspace\n",
    "def derivee (y,x) :\n",
    "    return 2 * x\n",
    "\n",
    "#  time points\n",
    "x = np.linspace ( 0 , 10)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 1\n",
    "\n",
    "# solve ODE\n",
    "solution = odeint ( derivee , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# plot results\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Equation diff y' = 2x - Solution : x² \" )\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()\n",
    "\n",
    "# Trouver la valeur au temps 10 avec l'interpolation graphique On voit que ce n'est pas le résultat précis\n",
    "print(\" Au temps 10, ma valeur sera de \" ,np.interp(10, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <b>Solution symbolique</b>\n",
    "\n",
    "Maintenant, on va chercher la solution de l'équation différentielle, avec les symboles mathématiques directement.\n",
    "\n",
    "On cherche toujours à résoudre :\n",
    "$$\n",
    "y'\n",
    "= 2x\n",
    "$$\n",
    "\n",
    "## Etape 1 : Entrer l'eq diff dans Sympy\n",
    "\n",
    "Ca permet à Sympy d'interpréter l'equation diff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2030,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 2 x$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 2*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "partie_gauche  = sympy.diff(y(x),x)\n",
    "partie_droite = 2 * x\n",
    "\n",
    "edo = sympy.Eq( partie_gauche , partie_droite )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Calculer la solution générale\n",
    "\n",
    "On calcule les fonctions solution de l'eq diff.\n",
    "On trouve bien la même solution que Yvan Monka.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2031,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} + x^{2}$"
      ],
      "text/plain": [
       "Eq(y(x), C1 + x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : Calculer une solution particulière\n",
    "\n",
    "Si on cherche x = 10 , on se sert de la solution générale trouvée juste au dessus dans l'étape 2, et c'est aussi évident sur le graphique. On trouve alors y = 100.\n",
    "On peut aussi afficher x = 3, pour voir, et on trouve 9.\n",
    "On substitue x par la valeur dans la solution générale.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2032,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Ma valeur au bout de 10 temps est de  100\n",
      " Ma valeur au bout de 3 temps est de  9\n"
     ]
    }
   ],
   "source": [
    "valeur = 10 ** 2\n",
    "print (\" Ma valeur au bout de 10 temps est de \" , valeur)\n",
    "\n",
    "valeur = 3 ** 2\n",
    "print (\" Ma valeur au bout de 3 temps est de \" , valeur)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <b>Solution algébrique avec DSolve</b>\n",
    "\n",
    "On se sert de dsolve pour résoudre \n",
    "$$\n",
    "y'\n",
    "= 2x\n",
    "$$\n",
    "\n",
    "Cela nous donne la solution générale, dans cet exemple, il n'y a pas de condition initiale, on va voir ça après...\n",
    "On vérifie les résultats et on voit bien qu'on trouve pareil qu'Yvan Monka, en solution logique, graphique, symbolique et algébrique, donc, ça prouve que les processus et codes sont bons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2033,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(y(x), C1 + x**2)\n",
      "C1 + x**2\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Function, Eq, dsolve\n",
    "\n",
    "# On paramêtre les symboles et fonction\n",
    "x = symbols('x')\n",
    "y = Function('y')\n",
    "\n",
    "# On entre l'équation différentielle dans SYMPY\n",
    "# Eq(PARTIE GAUCHE DE L'EQUATION DIFFERENTIELLE , PARTIE DROITE DE L'EQUATION DIFFERENTIELLE)\n",
    "equation_differentielle = Eq(Derivative(y(x), x) , 2*x)\n",
    "\n",
    "# On résouds l'équation différentielle, ça nous donne une solution générale\n",
    "result = dsolve(equation_differentielle)\n",
    "\n",
    "# affichage classique\n",
    "print(result)\n",
    "\n",
    "# affichage simplifié\n",
    "print(result.rhs)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparaison avec les suites géométriques\n",
    "\n",
    "Voir l'annexe en fin de fichier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <b><span style=\"color:green\">2. Résoudre une équation différentielle d'ordre 1 sans second membre -> y' = ay</span></b> \n",
    "-------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <strong>L'équation différentielle <span style=\"color:red\"> y'=2y<span></strong>\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\" La dérivée de la fonction y est égale à 2 fois la fonction y\"\n",
    "\n",
    "Ici, 2 est une <b>constante</b>, y est une <b>fonction</b>, y' est une <b>dérivée</b>.\n",
    "\n",
    "Lien : https://www.youtube.com/watch?v=qHF5kiDFkW8\n",
    "Lien : https://www.maths-et-tiques.fr/telech/20Prim-EdTC.pdf\n",
    "\n",
    "\n",
    "Voici La Notation fractionnaire qui veut dire la même chose et est plutôt utilisée en Sciences Physique .\n",
    "\n",
    "$$\n",
    "\\frac{dx}{dt}\n",
    "= 2 x(t)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Graphique \n",
    "\n",
    "La solution d'une eq diff est une fonction, on dessine donc une fonction !\n",
    "\n",
    "La fonction solution se dessine et prends forme suite au calcul de ces dérivées successives sur l'intervalle [0;10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2034,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Au temps 9, ma valeur sera de  66211191.82837978\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# fonction qui retourne la dérivée pour chaque x fourni à la fonction np.linspace\n",
    "def derivee (y,x) :\n",
    "    return 2 * y\n",
    "\n",
    "#  time points\n",
    "x = np.linspace ( 0 , 10)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 1\n",
    "\n",
    "# solve ODE\n",
    "solution = odeint ( derivee , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# plot results\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Equation diff y' = 2y \" )\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()\n",
    "\n",
    "# Trouver la valeur au temps 9 avec l'interpolation graphique\n",
    "# On voit que ce n'est pas le résultat précis, il faut trouver une autre méthode\n",
    "print(\" Au temps 9, ma valeur sera de \" ,np.interp(9, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution symbolique\n",
    "\n",
    "Maintenant, on va résoudre avec les symboles mathématiques et voir si on trouve le même résultat pour une valeur de x = 9 !\n",
    "\n",
    "## Etape 1 : Entrer l'eq diff dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2035,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 2 y{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 2*y(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "right = 2 * y(x) # y(x) est bien une fonction\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Calcul de la Solution générale\n",
    "\n",
    "L'equation différentielle est au format y' = ay\n",
    "\n",
    "On trouve bien la même solution que Yvan Monka.\n",
    "\n",
    "Les solutions de l'equation différentielle sont les fonctions suivantes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2036,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{2 x}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(2*x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : Calcul d'une solution particulière\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2037,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Ma valeur au bout du temps 9 est de  65659969.13733051\n"
     ]
    }
   ],
   "source": [
    "# Afficher une solution particullière en utilisant l'eq de la solution générale\n",
    "# Notre valeur au temps 9\n",
    "import math \n",
    "valeur = math.exp(2 * 9)\n",
    "print (\" Ma valeur au bout du temps 9 est de \" , valeur)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Algébrique avec Dsolve\n",
    "\n",
    "On se sert de dsolve pour résoudre \n",
    "$$\n",
    "y'\n",
    "= 2y\n",
    "$$\n",
    "\n",
    "Cela nous donne la solution générale, dans cet exemple, il n'y a pas de condition initiale, on va voir ça après..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2038,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eq(y(x), C1*exp(2*x))\n",
      "C1*exp(2*x)\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Function, Eq, dsolve\n",
    "\n",
    "# On paramêtre les symboles et fonction\n",
    "x = symbols('x')\n",
    "y = Function('y')\n",
    "\n",
    "# On entre l'équation différentielle dans SYMPY\n",
    "# Eq(PARTIE GAUCHE DE L'EQUATION DIFFERENTIELLE , PARTIE DROITE DE L'EQUATION DIFFERENTIELLE)\n",
    "equation_differentielle = Eq(Derivative(y(x), x) , 2 * y(x))\n",
    "\n",
    "# On résouds l'équation différentielle\n",
    "result = dsolve(equation_differentielle)\n",
    "\n",
    "# affichage classique\n",
    "print(result)\n",
    "\n",
    "# affichage simplifié\n",
    "print(result.rhs)\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <strong>L'équation différentielle <span style=\"color:red\">5y' + 2y =0<span></strong>\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "Lien :  https://www.letudiant.fr/lycee/methodologie-lycee/article/equations-differentielles-entrainez-vous-avec-nos-exercices-corriges.html\n",
    "\n",
    "<center><img src=\"img/pb.png\"></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Déterminer la solution générale de cette équation avec Sympy\n",
    "\n",
    "\n",
    "\n",
    "On la mets d'abord au format \"standard\" avec la dérivée à gauche : \n",
    "\n",
    "$$ y' = \\frac{-2 * y } {5}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 1 : Entrer l'eq diff dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2039,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = - \\frac{2 y{\\left(x \\right)}}{5}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), -2*y(x)/5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "\n",
    "right = -2 * y(x) / 5 # La fonction y s'écrit y(x)\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Calcul de la Solution générale\n",
    "\n",
    "L’ensemble des solutions s’écrit sous la forme yc(x) = Ce *a.x , C appartient à R\n",
    "On trouve bien la même solution que dans le magazine l'étudiant.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2040,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{- \\frac{2 x}{5}}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(-2*x/5))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Déterminer l’unique solution de l’équation telle que y(1) = 3 avec Sympy\n",
    "\n",
    "Autrement dit, déterminer l'unique fonction solution de l'équation différentielle, quand y(1) = 3\n",
    "\n",
    "## Etape 1 :  Entrer la condition\n",
    "\n",
    "La condition est une constante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2041,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: 3*exp(2/5)}"
      ]
     },
     "execution_count": 2041,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 1\n",
    "y1 = 3\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Calculer La solution unique avec la constante\n",
    "\n",
    "On prends en compte la constante définie précédemment.\n",
    "On voit qu'on trouve la même solution que dans l'exercice ."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2042,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Unique solution telle que 𝑓(1) = 3'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = 3 e^{\\frac{2}{5}} e^{- \\frac{2 x}{5}}$"
      ],
      "text/plain": [
       "Eq(y(x), 3*exp(2/5)*exp(-2*x/5))"
      ]
     },
     "execution_count": 2042,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "\n",
    "display(\"Unique solution telle que 𝑓(1) = 3\")\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <strong>L'équation différentielle <span style=\"color:red\"> 3𝑦' + 5𝑦 = 0<span></strong>\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "On considère l’équation différentielle 3𝑦' + 5𝑦 = 0.\n",
    "\n",
    "- 1) Déterminer la forme générale des fonctions solutions de l’équation.\n",
    "\n",
    "- 2) Déterminer l’unique solution 𝑓 telle que 𝑓(1) = 2.\n",
    "\n",
    "Lien : https://www.maths-et-tiques.fr/telech/20Prim-EdTC.pdf\n",
    "\n",
    "On retrouve le même résultat !\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2043,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\" Affichage de l'eq diff\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = - \\frac{5 y{\\left(x \\right)}}{3}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), -5*y(x)/3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "' Solution générale'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{- \\frac{5 x}{3}}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(-5*x/3))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'Unique solution telle que 𝑓(1) = 2'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = 2 e^{\\frac{5}{3}} e^{- \\frac{5 x}{3}}$"
      ],
      "text/plain": [
       "Eq(y(x), 2*exp(5/3)*exp(-5*x/3))"
      ]
     },
     "execution_count": 2043,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "right = -5 * y(x) / 3 # La fonction y s'écrit y(x)\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(\" Affichage de l'eq diff\",edo)\n",
    "\n",
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(\" Solution générale\",solgen)\n",
    "\n",
    "x0 = 1\n",
    "y1 = 2\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts\n",
    "solpar = solgen.subs(consts)\n",
    "display(\"Unique solution telle que 𝑓(1) = 2\")\n",
    "solpar\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <strong>L'équation différentielle <span style=\"color:red\"> dy/dt = -yt + 13<span></strong>\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\\begin{cases}\n",
    "\\frac{dy}{dt}\n",
    "= -yt + 13\n",
    "\\end{cases} \n",
    "\n",
    "## Résoudre graphiquement"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2044,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import numpy as np \n",
    "from scipy.integrate import odeint \n",
    "import matplotlib.pyplot as plt \n",
    "  \n",
    "def returns_dydt(y,t): \n",
    "    dydt = -y * t + 13\n",
    "    return dydt \n",
    "  \n",
    "# initial condition \n",
    "y0 = 1\n",
    "  \n",
    "# values of time \n",
    "t = np.linspace(0,5) \n",
    "  \n",
    "# solving ODE \n",
    "y = odeint(returns_dydt, y0, t) \n",
    "  \n",
    "# plot results \n",
    "plt.plot(t,y) \n",
    "plt.xlabel(\"Time\") \n",
    "plt.ylabel(\"Y\") \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Le problème de Cauchy\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "\\begin{cases}\n",
    "u'(x)=-3x^2u(x)+6x^2,\\\\\n",
    "u(0)=4.\n",
    "\\end{cases}\n",
    "\n",
    "On remarque que maintenant, il y a une condition initiale, c'est pour cela qu'on l'appelle \" Problème de Cauchy\"."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Graphique (Numérique)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2045,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import des libs\n",
    "from scipy import *\n",
    "from scipy.integrate import odeint #Pour résoudre l’équation différentielle\n",
    "import matplotlib.pyplot as plt # Permet de tracer des graphes\n",
    "import numpy as np\n",
    "from math import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2046,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Equation\n",
    "def deriv (y,x) :\n",
    "    return 6*x**2 - 3*x**2 * y\n",
    "\n",
    "# Choix de l’ intervalle d’intégration\n",
    "x0 = 0\n",
    "xmax = 20\n",
    "npoints = 1000\n",
    "x = np.linspace ( x0 , xmax , npoints )\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 4 # y(x0) = y0\n",
    "\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "plt.plot ( x , y )\n",
    "plt.show ( )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Symbolique\n",
    "\n",
    "Le problème de Cauchy:\n",
    "\\begin{cases}\n",
    "u'(x)=-3x^2u(x)+6x^2,\\\\\n",
    "u(0)=4.\n",
    "\\end{cases}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 1 : Entrer l'eq diff dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2047,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} u{\\left(x \\right)} = - 3 x^{2} u{\\left(x \\right)} + 6 x^{2}$"
      ],
      "text/plain": [
       "Eq(Derivative(u(x), x), -3*x**2*u(x) + 6*x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "u   = sympy.Function('u')\n",
    "\n",
    "left  = sympy.diff(u(x),x)\n",
    "\n",
    "right = 6*x**2 - 3*x**2 * u(x)\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Calculer la solution générale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2048,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle u{\\left(x \\right)} = C_{1} e^{- x^{3}} + 2$"
      ],
      "text/plain": [
       "Eq(u(x), C1*exp(-x**3) + 2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,u(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : Prendre en compte les conditions initiale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2049,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: 2}"
      ]
     },
     "execution_count": 2049,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 0\n",
    "u0 = 4\n",
    "consts = sympy.solve( sympy.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 4 : Solution avec les conditions initiales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2050,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle u{\\left(x \\right)} = 2 + 2 e^{- x^{3}}$"
      ],
      "text/plain": [
       "Eq(u(x), 2 + 2*exp(-x**3))"
      ]
     },
     "execution_count": 2050,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 5 : Solution graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2051,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "func = sympy.lambdify(x,solpar.rhs,'numpy')\n",
    "from matplotlib.pylab import *\n",
    "# rcdefaults()\n",
    "rcParams.update({'font.size': 16})\n",
    "figure(figsize=(10,7))\n",
    "xx=linspace(0,3,101)\n",
    "yy=func(xx)\n",
    "plot(xx,yy)\n",
    "xlabel('x')\n",
    "ylabel('u')\n",
    "grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Des sin et des cos\n",
    "-------------------------------------------------------------------------------------------------------\n",
    "\n",
    "\\begin{cases}\n",
    "t'(x)=sin(t) * sin(x)\n",
    "\n",
    "\\end{cases}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## Solution Graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2052,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2053,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def f(x, t):\n",
    "    return np.sin(t) * np.sin(x)\n",
    "t = np.linspace(0, 50, 256)\n",
    "x = odeint(f, 1, t)\n",
    "plt.plot(t, x)\n",
    "plt.title(\"solution de x'=sin(t)sin(x)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution symbolique\n",
    "\n",
    "## Etape 1 : Entrer l'eq diff dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2054,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = \\sin{\\left(x \\right)} \\sin{\\left(y{\\left(x \\right)} \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), sin(x)*sin(y(x)))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x) # Partie gauche, avec la dérivée\n",
    "\n",
    "right = sympy.sin(y(x)) * sympy.sin(x) # Partie droite, avec les sin et cos qui fonctionnent.\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Cas pratique 1 :  Croissance constante linéaire\n",
    "\n",
    "------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Description\n",
    "\n",
    "Cette forme de croissance est la plus simple et nous offre un excellent moyen de nous entraîner à traduire la théorie en mathématiques.\n",
    "\n",
    "Supposons que nous ayons une théorie selon laquelle une variable change de manière constante. Par exemple, nous pourrions modéliser le montant d’argent sur un compte d’épargne, si 10 euros étaient <b>ajoutés</b> chaque jour. La variation du solde du compte est toujours de 10 euros/jour, quels que soient les soldes passés ou actuels.\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/compte-epargne.png\">\n",
    "</div>\n",
    "\n",
    "Voici la représentation mathématique:\n",
    "\n",
    "\\begin{cases}\n",
    "\\frac{dx}{dt}\n",
    "= 10\n",
    "\\end{cases} \n",
    "\n",
    "Ou dt est une journée.\n",
    "\n",
    "On peut l'écrire y' = 10 ( A vérifier)\n",
    "\n",
    "<b>Le problème est donc de trouver la fonction dont la dérivée est égale à 10</b>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Logique\n",
    "\n",
    "En regardant le tableau usuel des dérivées, on constate que la fonction solution de l'eq diff est f(x) = 10x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2055,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Equation qui retourne la dérivée pour chaque point de np.linspace\n",
    "def deriv (y,x) :\n",
    "    return 10\n",
    "\n",
    "# Choix de l’ intervalle d’intégration\n",
    "x0 = 0\n",
    "xmax = 20\n",
    "npoints = 1000\n",
    "x = np.linspace ( x0 , xmax , npoints )\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 1\n",
    "\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Compte épargne\")\n",
    "plt.ylabel(\"montant\")\n",
    "plt.xlabel(\"jours\")\n",
    "plt.show ( )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution symbolique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2056,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 10$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 10)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} + 10 x$"
      ],
      "text/plain": [
       "Eq(y(x), C1 + 10*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "right = 10\n",
    "\n",
    "# Etape 1 Afficher l'equation différentielle\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)\n",
    "\n",
    "# Etape 2  Afficher la solution générale\n",
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)\n",
    "\n",
    "# Etape 3  Donner la condition initiale\n",
    "x0 = 0\n",
    "y1 = 0\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts\n",
    "\n",
    "# Etape 4 Afficher l'équation du capital en fonction du temps\n",
    "solpar = solgen.subs(consts)\n",
    "solpar\n",
    "\n",
    "# Etape 5 Afficher le capital au jour 5 \n",
    "capital = 10 * 5\n",
    "print (capital)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cas pratique 2 : Croissance exponentielle</b>\n",
    "-------------------------------------------------------------------------------------\n",
    "\n",
    "\n",
    "## Example des lapins\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/lapins.jpg\">\n",
    "</div>\n",
    "\n",
    "Supposons qu'on ait 100 lapins au temps t0 ( Condition initiale = 100) et que le taux de croissance soit de 20% .\n",
    "\n",
    "L'équation différentielle qui résume cette situation ( A vérifier) : \n",
    "\n",
    " $$\\frac{dP}{dt}=k * dP$$ \n",
    "autrement écrit ( A vérifier): $$ y'= k * P(x)$$  \n",
    "\n",
    "  avec\n",
    "\n",
    "  $$ t(0) = 100 , t ∈ [0, 4] $$\n",
    "\n",
    "où ( Nomenclature )\n",
    "\n",
    " - dP/dt qui est l'évolution de la population en fonction du temps\n",
    " - k qui est le taux de croissance de la population\n",
    " - t(0) qui est la population de lapins au temps 0\n",
    " - [ 0, 4 ] qui est le nombre de pas de temps, ou l'étendue du phénomène étudié.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant, on veut savoir comment va évoluer la population\n",
    " - Graphiquement\n",
    " - Symboliquement\n",
    "\n",
    " Note : Une suite géométrique donnera un résultat différent\n",
    "\n",
    " ## Solution graphique\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2057,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --------------------------------------------------------------------------------------------------------------\n",
    "# Un premier code, qui fonctionne, mais difficile à lire.\n",
    "# --------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "\n",
    "# Etat du système à t0  \n",
    "z0 = np.array([100]) # On débute avec 100 lapins\n",
    "alpha = 0.2 # Le taux de croissance\n",
    "\n",
    "f = lambda t, z : alpha * z\n",
    "\n",
    "# Timespan = intervalle de temps étudiée t_span - a tuple (t0, t1) which gives the start and end times of the simulation\n",
    "t_span = (0, 100)\n",
    "t_eval = np.linspace(0,4, 100)\n",
    "\n",
    "sol = solve_ivp(f, t_span, z0, t_eval=t_eval)\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot(sol.t, sol.y[0], c='k')\n",
    "plt.title(\"Population de lapins\")\n",
    "plt.ylabel(\"lapins\")\n",
    "plt.xlabel(\"jours\")\n",
    "plt.show()\n",
    "\n",
    "# --------------------------------------------------------------------------------------------------------------\n",
    "# Maintenant un code plus simple, qui fait la même chose...\n",
    "# Désormais, on utilisera plus que celui là !\n",
    "# --------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "# Taux de croissance des lapins\n",
    "k = 0.2\n",
    "\n",
    "# Equation différentielle\n",
    "def deriv (y,x) :\n",
    "    return   y * k\n",
    "\n",
    "#  Intervalle de temps\n",
    "x = np.linspace ( 0 , 4)\n",
    "\n",
    "# Condition initiale : 100 lapins\n",
    "y0 = 100\n",
    "\n",
    "# Résoudre l'équation diff\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Population de lapins\")\n",
    "plt.ylabel(\"lapins\")\n",
    "plt.xlabel(\"jours\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution symbolique avec SYMPY\n",
    "\n",
    "Etape 1 : Entrer l'eq diff dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2058,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 0.2 y{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 0.2*y(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "k = 0.2 # taux\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x) # Veut dire \" la dérivée\"\n",
    "right = k * y(x) # La partie droite de l'équation différentielle, on réécrit la formule mathématique plus haut.\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Trouver la solution générale de l'eq diff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2059,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{0.2 x}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(0.2*x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 3 : Déterminer l’unique solution de l’équation telle que T(0) = 100 avec Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2060,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: 100}"
      ]
     },
     "execution_count": 2060,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 0\n",
    "y1 = 100\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 4 : Equation de la population des lapins en fonction du temps\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2061,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = 100 e^{0.2 x}$"
      ],
      "text/plain": [
       "Eq(y(x), 100*exp(0.2*x))"
      ]
     },
     "execution_count": 2061,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 5 : Quelle sera la population de lapins après 4 jours ?\n",
    "\n",
    "On utilise l'équation trouvée à l'étape 4 pour demander quelle sera la population de lapins au jour 4.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2062,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " La population de lapins au bout de 4 jours sera   222.55409284924679 lapins\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "population = 100 * math.exp(0.2 * 4)\n",
    "print(\" La population de lapins au bout de 4 jours sera  \",population,\"lapins\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemple 2.1 : Croissance de bactéries et interpolation\n",
    "-------------------------------------------------------------------------------------\n",
    "\n",
    "Au début de l'expérimentation, il y a 100 bactéries. Si les bactéries suivent un modèle de croissance avec un taux k = 0.2,\n",
    "trouver la population après 5 heures, puis après 10 heures.\n",
    "ON va essayer de voir si on peut, grâce à une interpolation graphique, trouver un résultat correct."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2063,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " au temps 5, ma populaton sera de  271.88479583410134\n",
      " au temps 10, ma populaton sera de  738.905626502641\n"
     ]
    }
   ],
   "source": [
    "# Taux de croissance\n",
    "k = 0.2\n",
    "\n",
    "# Equation différentielle\n",
    "def deriv (y,x) :\n",
    "    return y * k\n",
    "\n",
    "#  Etendue du temps étudié\n",
    "x = np.linspace ( 0 , 10)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 100\n",
    "\n",
    "# Résoudre l'équation diff\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Bactéries\" )\n",
    "plt.ylabel(\"nombre\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "# Trouver la valeur des bactéries au temps 5 \n",
    "# L'interpolation graphique n'est pas précise, trouver une autre méthode\n",
    "print(\" au temps 5, ma populaton sera de \" ,np.interp(5, x, y))\n",
    "\n",
    "\n",
    "# Trouver la valeur des bactéries au temps 10\n",
    "print(\" au temps 10, ma populaton sera de \" ,np.interp(10, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemple 2.2 : Solution chimique  et temps exact avant de trouver un résultat précis\n",
    "---------------------------------------------------------------------------------------------------------\n",
    "\n",
    "Trouver au bout de combien de temps la valeur de y se réduira à 1\n",
    "\n",
    "https://kitchingroup.cheme.cmu.edu/blog/2011/08/31/Solving-an-ode-for-a-specific-solution-value/\n",
    "\n",
    "\n",
    "La solution analytique d'une ODE est une fonction qui peut être résolue pour obtenir une valeur particulière, par ex. si la solution d'une ODE est y(x) = exp(x), vous pouvez résoudre la solution pour trouver la valeur de x qui fait y(x)=2\n",
    "\n",
    ". Dans une solution numérique d'une ODE, nous obtenons un vecteur de valeurs de variables indépendantes et les valeurs de fonction correspondantes à ces valeurs. Pour résoudre une valeur de fonction particulière, nous avons besoin d’une approche différente. Cet article montrera une façon de le faire en python.\n",
    "\n",
    "Étant donné que la concentration d'une espèce A dans un volume constant, le réacteur discontinu obéit à cette équation différentielle $$\\frac{dC_A}{dt}=- k C_A^2$$ avec la condition initiale CA(t=0)=2,3 mol/L et k=0,23 L/mol/s, calculez le temps qu'il faut pour CA\n",
    "à réduire à 1 mol/L.\n",
    "\n",
    "Nous obtiendrons une solution, puis créerons une fonction d'interpolation et utiliserons fsolve pour obtenir la réponse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2064,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import odeint\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.optimize import fsolve\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "k = 0.23\n",
    "Ca0 = 2.3\n",
    "\n",
    "def dCadt(Ca, t):\n",
    "    return -k * Ca**2\n",
    "\n",
    "tspan = np.linspace(0, 10)\n",
    "\n",
    "sol = odeint(dCadt, Ca0, tspan)\n",
    "Ca = sol[:,0]\n",
    "\n",
    "plt.plot(tspan, Ca)\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('$C_A$ (mol/L)')\n",
    "\n",
    "\n",
    "ca_func = interp1d(tspan, Ca, 'cubic')\n",
    "\n",
    "itime = np.linspace(0, 10, 200)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(tspan, Ca, '.')\n",
    "plt.plot(itime, ca_func(itime), 'b-')\n",
    "\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel('$C_A$ (mol/L)')\n",
    "plt.legend(['solution','interpolated'])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2065,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.4574668234994648\n"
     ]
    }
   ],
   "source": [
    "tguess = 2.0\n",
    "tsol, = fsolve(lambda t: 1.0 - ca_func(t), tguess)\n",
    "print (tsol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemple 2.3  : Tracer plusieurs eq diffs avec un différent taux k pour les comparer.\n",
    "\n",
    "Ca peut être utile lors de l'analyse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2066,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y(t)')"
      ]
     },
     "execution_count": 2066,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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++yx79+7liy++oECBAlf8+ri4OKKjo10edtl2YhuvLXqNn7b+xNL9SzP9uoCALEpoUgQHmyrDKcNAmzaZGjZJSVn4piIiIu7nsUnN3Llz+eqrr7j77ru5/fbbr+oaQ4cOJSwsLPURHh7u3iCvQN1idVO3M1OAL1sVKAC//mr+BDN5Z9Age2MSERG5Qh6Z1ERFRfHggw9SpEgRhg8fftXXeeGFF4iKikp9REREuDHKK1M2f1l+7PEj257YxpQ7plzVNWJiTCE+t04YTlG5MkybBkH/3ZH85BP4+usseCMREZGs4ZFzagYOHMiBAweYPHkyhQsXvurrhISEEBJy5Uups0KAI4A7at5x1a/ftw9q14YzZ6BpU+eqKLdq2xY+/9ysJQd4/HGoVMkcFxER8XAOKzMdFrNZ/vz5OXv2LM2bN093btu2bRw9epRy5cpRtmxZihcvzqRJkzJ13ejoaMLCwoiKiiKfl02EtSyoVw82bDD7a9ZA/fpZ9GZPP21GasDckvrrryxYeiUiIpI5mf3+9tikJioqKlPPLVu2LPsyuQzZm5MaMB27U3pCPfSQKciXJZKS4LbbnPe5qlQxic1VTNYWERG5Vpn9/vbIOTWnT5/GsqwMH/fffz8Ab731FpZlZTqh8QSJyYmsPbyWMevGMHnT5Ct+/T33QJ48Znv8eDh1ys0BpggMhAkToFYts79jh2mEGReXRW8oIiJy7TwyqfFV5xPPc92o6+g7oy8f//Xx5V9wgbx54b+cjtjYLBypAVOnZuZMKFrU7C9aBA88YO6DiYiIeCAlNdkoT448VCxYEYCNRzeSlHzltWCefNLUzAMYNswUAs4y5cqZhpe5cpn9CRPg5Zez8A1FRESunpKabDag8QA+aP8BM+6egcWVj3pUrgxdupjtQ4dM3bws1aQJTJzozKSGDMniISIREZGr45EThbOKt08UTvHnn9C6tdmuXx/++ceZc2SZESPgf/8z24GBZgTHD3txiYhI9vPqicJyaS1bwnXXme2tW03rpizXvz8884zZTkqCO+8068pFREQ8hJIaL+RwwKuvwltvQUSEuSWVLd5/H3r0MNtnz5oKgP/+m01vLiIicmm6/WSTyNhItp7YSosyLWyN44qdPw833mg6eQNUr262VcNGRESyiG4/ebCuk7tS+IPCtPyuJafOZVWxmSySMyfMmOEcHtq6VTVsRETEIyipsUHJPCVTtzce2+iWa8bEmEe2KFQIfvsNihQx+6phIyIiHkBJjQ2uD7+e1mVb87/G/6NQrkLXdK2jR2HQIChd2tStyTYVK5rifGlr2Lz4YjYGICIi4kpzarzcnj3mTlByMhQvbrp5Z2tj8hkzoGtX5yjNp5+aCoEiIiJuojk1fqJCBZNTABw5AplsWO4+t90Gw4c79wcONKM2IiIi2UxJjQ9IKR8D8NFHNkxteeIJeOUV5/7998Pvv2dzECIi4u+U1Ngs2UomISnhmq5x/fXQtKnZ3rgR5s93Q2BX6o034JFHzHZiInTvDqtW2RCIiIj4KyU1Npm1YxbNRjcj7N0wpm+bfs3Xe/pp5/bHV94A/No5HDBypElmwBTn69QJtm2zIRgREfFHSmpskpicyIoDKzgTf4YNRzdc8/W6doWyZc32b7/Bli3XfMkrFxgI48ZBmzZmPzISOnSAAwdsCEZERPyNkhqb1ClWB4By+cuRKyjXNV8vKMh10dEnn1zzJa9OSnG++vXNfkQE3HQTnDxpU0AiIuIvtKTbJpZlER0XTVjOMLddMzoawsPNnyEhsH8/FC3qtstfmaNHoXlz2L3b7DdrBvPmQe7cNgUkIiLeSku6PZzD4XBrQgOQLx889BAUKwYvvww5crj18lemWDGYO9f8CbB8uensnXBtk6JFREQuRiM1PiYqytwBytYCfJeybh20bm2GjwDuvRfGjIEA5dMiIpI5GqnxU2FhHpTQANSrB7/84gzqhx9gwAD1iRIREbdTUmOjqPNRDFkyhLun3s3ri163O5ys07q1KXUcGGj2R45UnygREXE7JTU2CgoI4uUFLzN582Rm75zt9usfOOBBXQtuv93cdkrx7rswZIhd0YiIiA8KsjsAfxaaI5RKBSux8+ROdp7cSbKVTIDDPXnm3r1QrRrEx5uGl3fd5RwosU3v3hATA48/bvZfegny5DG3o0RERK6RRmpsNrrLaDY9toljzx5zW0IDUL68WVENsHMnTJnitktfm8ceg/ffd+4/+SR8+6198YiIiM9QUmOzlmVbUrNoTYIDg91+7Zdfdm6/8w4kJ7v9La7OoEGuDTAfegh+/NG+eERExCcoqfFhbduaZpcAmzaZRUge4403zIQfMNnWPffAr7/aGpKIiHg3JTU+zOFwHa15+20PWkntcJjOm/36mf3EROjRAxYssDcuERHxWkpqPMDW41sZv2E8b//5ttuvffPNzjZM//wDv//u9re4eg4HfPkl3H232Y+Lgy5dYMUKe+MSERGvpKTGAzz868P0nt6bVxa+wqlzp9x67QtHa956y4NGa8Asyfr+e+jc2eyfPWsysX/+sTcuERHxOkpqPEDdYnVTtzce2+j2699+O9SoYbaXL4fFi93+FtcmONhMFL7hBrMfFQXt28PatfbGJSIiXkVJjQfoVr0bQ28Yyqxes1wSHHcJCDAlYQBKloRT7h0Mco+cOeHnn6FlS7N/6hTceCOsX29rWCIi4j3U0NJPJCbC+PFm+opH9Ya6UEyMuf20bJnZL1TITB6uU8feuERExDZqaCkugoLg/vs9PKEByJsXZs92rkWPjDS3pTZtsjcuERHxeEpqxPPkywdz5kCTJmb/xAlo1w62bLE3LhER8WhKajzI6fOnWfLvEiJjI7P8vfbuha++yvK3uXr58pn1540amf3jx01is3WrvXGJiIjHUlLjIT7961MKvFeAVmNaMX/v/Cx9r+eeM00uH30UNm/O0re6NmFhMHcuXHed2T961CQ227fbG5eIiHgkJTUeokKBCqnb649k7Yqf4sUhKclsDx2apW917fLnh3nzoEEDs3/kiOn/sGOHrWGJiIjnUVLjIeoVr0ez8GY8et2jtCjTIkvf65FHzKIigIkTTRdvj1aggEls6tUz+4cPm8TG4wMXEZHspCXdfmrIEGftmt694Ycf7I0nUyIjze2nDRvMfvHiZrl39er2xiUiIllKS7rlkvr3h4IFzfb48V6yYrpQIZg/31mz5sgRaN3ameSIiIhfU1Ljp/LlgxdeMNuW5dofyqMVLmxGZ1Lm2Bw/bm5FrVljb1wiImI7JTUeKCk5iaNnjmb5+zzxhGmbADBjBqxcmeVv6R4pIzYpdWxOnjQF+rzmLyAiIllBSY0HSUhK4KZxN1Hw/YJ0mdQly98vVy549VXn/osvZvlbuk/+/Ga5d4v/JlWfPm2aYC5damdUIiJiIyU1HiQ4MJj9UfuJjotm7eG1nE88n+Xv+cADULGi2Y6IMMV7vUZK5eF27cx+TAx07AgLF9obl4iI2EJJjYe5vvT1lMhTgs5VO3PqXNa30w4Oho8/hm++MV0IChfO8rd0r9BQ+PVXuOkms3/2LHTqZKoRi4iIX9GSbg9zLuEcOYNy4nA47A7Fu5w/D3feCTNnmv0cOWDaNLj1VnvjEhGRa6Yl3V4qV3AuJTRXI2dOmDoVunc3+/Hx0K2bSWxERMQvKKmRdDZs8NJpKTlywKRJ0LOn2U9IMKM3335rb1wiIpItlNR4uOy8OxgXB/fcY7oRPPigGezwOkFBpjxy375mPznZ/GU+/tjeuEREJMspqfFAqw+t5r7p91F5eGUmbZqUbe8bEmJq2VkW7N1rJg97pcBAE/zAgc5jzzxjKgz6zxQyERG/o6TGA0XGRvLDhh/YdXIXyyOWZ+t7Dxni3H7rLbOYyCsFBJjRmbfech575x3THyI52b64REQkyyip8UBNSptKuSGBIZxLPJet792woZlfC6a10ogR2fr27uVwmNGZ4cOdxz7/HO6918y3ERERn6Il3R5q7eG11ChSg5CgkGx/7y1boHZtM6BRoADs2WMK+Hq1ceOgTx9ISjL7t9wCU6aYssoiIuLRvH5J9/jx47nvvvuoW7cuRYsWJTg4mLCwMBo3bszQoUM5c+aM3SFmqfol6tuS0ADUqGEGMwBOnYIPPrAlDPfq3Rt++slMHAKYNctUH46OtjcuERFxG48dqWnRogXLly+nevXqhIeHU7BgQY4ePcqKFSs4d+4clSpVYvHixZRM6ciYCd40UmO3ffugShVzlyZ3bjNaU6yY3VG5wcKF0KULpCTFDRqYVgtFitgbl4iIXJTXj9R89NFHnDhxgs2bNzNnzhwmTJjA/PnziYiIoEWLFuzatYtnnnnG7jB9Vrly8MgjZjs21nW+rVdr29YkNoUKmf01a0xTzL177Y1LRESumceO1FzKkiVLaNWqFQULFiQyMjLTr/O2kZo5u+awYO8Ctp3Yxoy7Z2R7peGjR02zy7NnoVkzWLzYlIHxCVu2QIcOcPCg2S9eHGbPhvr17Y1LRETSyez3t1d+RQX9980aEmLPnJPs8tnKz5izaw4Ae0/vpUKBCtn6/sWKwfvvm2bYvXqZVdI+o0YNWLbMzKvZts0s9Wrd2sy7ufFGu6MTEZGr4HVfUzExMbz++usAdOnSxd5gstj1pa9P3V57eK0tMTz+uJlj61MJTYqyZWHpUrj+v3/nmBjT4XvCBHvjEhGRq+LxIzVz585lwoQJJCcnp04UjomJoWPHjrz33nuXfG1cXBxxcXGp+9FettLlrpp3UadYHa4vfT3F8vjCLF0PVKgQ/PGH6Rf1yy9mZvQ998Dhw6YKsYiIeA2PT2q2bNnC2LFjXY716tWLjz/+mLCwsEu+dujQobzxxhtZGV6Wqlq4KlULV7U7DBd//mnm2txxh92RuFHu3Kabd//+8NVX5tizz5r5Nh9+6KPDVCIivsdrJgonJCSwf/9+ZsyYwdtvv43D4WD69Om0atXqoq/JaKQmPDzcayYKe5LERDOvZsoUU5Bv1y4oWNDuqNzMsuDtt+HVV53H7r4bxoxx1rcREZFs5/VLui8UHBxMxYoVefrpp/ntt984deoUvXv35ty5i7cRCAkJIV++fC4PuTpBQZAzp9k+dQrefNPeeLKEwwGvvAJff22aYgJMmgQ33wxRUfbGJiIil+U1SU1aTZo0oUaNGkRERLB69Wq7w8lS8Unx/HXgLz5Z8Qkzts2wNZYhQ8ydGoCRI82iIZ/Urx/8/LOzhcLChdCqFURE2BqWiIhcmlcmNQChoaEAHDt2zOZIstaeU3u4fvT1PD33ab5d962tsZQuDc8/b7YTE820E591662wYIGzSN+GDdCkiSnWJyIiHskrk5oTJ06wfv16AKpUqWJzNFmrSqEqFMhZAIDlEcuxewrUs8+a5AZM+6Tff7c1nKzVtCksXw4V/qsPdPgwtGwJM2faG5eIiGTII5OaLVu2MH78eM6fP5/u3I4dO7jjjjuIi4ujadOm1K5d24YIs0+AI4CXWr7E550+Z9698+wOh9y5Ie1K+qefNqM2PqtKFfjrL1NSGUzPiNtug2HD7I1LRETS8cjVT4sWLaJt27aEhoZSv359SpcuTXx8PPv372fNmjUkJydTvXp15syZQ5kyZTJ9XW9rk+CpLMt8x//1l9kfOdIU6fNp589Dnz4webLzWP/+8MknPtQ7QkTEM2X2+9sjk5rjx4/z9ddfs2TJErZt28bx48dJSEigYMGC1K5dm27dutG3b98rbpOgpMZ9/vrLWYi3UCHYudMs9fZpyclmufc77ziP3XKLWSGVJ499cYmI+DivTmqyipIa9+rdG8aPhzZt4LvvTGdvv/Ddd/Dww877bvXqwa+/QqlStoYlIuKrfK5Ojb+zLIt/T//LpE2TOBN/xu5wABg6FKZPN4uE/CahAejb18yQzp/f7K9bZ1ZGrVtnY1AiIqKkxks8N+85yn1Wjp7TerLq4Cq7wwEgPBxuv93UrPM77dqZlVHly5v9gwehRQuYYW8tIRERf6akxkvULuZc5bUiYoWNkUiq6tXN5KKmTc3+2bMmy3vnHTObWkREspWSGi/RPLw5N1a4kVdavcJNlW6yO5wM/fYbtG4NMTF2R5KNihY199969nQee/ll0yjrEi08RETE/TRRWNzivfdg8GCz/dRT8PHH9saT7SwL3n0XXnzReey668ztKE0gFhG5JpooLNnqjjucDS8/+wzWrrU3nmzncMALL5ieUf+18OCff6BhQ1i50tbQRET8hZIacYsKFUyDazDlXB59FJKS7I3JFrfdBitWOJeDHTli7smNH29rWCIi/kBJjRc6G3+WnZE77Q4jnWefNXNnAVatglGj7I3HNrVrm3+AVq3MflycKeozeLCfZnoiItnDLUnNmTNn2L17N6tXr2b37t2cOeMZdVR8TVJyEk2+aULYu2H0mNLD7nDSyZEDvvzSuf/CC2agwi8VKQLz5pkifSnee8+sjoqOti0sERFfdtVJze+//85jjz1GlSpVCAsLo0qVKjRp0iR1v2rVqjz22GP87tNtnLNXYEAg8UnxJFlJbDq2idPnT9sdUjqtWpkWSQBRUabhpd9KyfKGD4fAQHPs11+hcWPYutXe2EREfNAVJTVJSUmMGDGCKlWq0KlTJ7766it27dqFZVmEhoZSokQJcufOjWVZ7Ny5k6+++opOnTpRtWpVRo4cSZKG3q9Z67KtqVqoKk80eoLziem7mHuCDz6AggXN9sSJZsDCbzkcpvHlnDnO5ljbt5vE5qef7I1NRMTHZHpJ95w5c3jqqafYvn07wcHBdOrUifbt29OsWTNq1qxJcHBw6nPj4+PZtGkTy5cvZ968ecyZM4fExESqVq3KJ598wk032VNnxReWdCckJRAcGHz5J9rs22/hwQfNdp06poOAX1YeTmv3bujWDTZscB574QV46y3nSI6IiKTj9oaWAQEBFCtWjEGDBnHfffdRuHDhTAdz4sQJxo4dy/vvv8+JEydsG7HxhaTGWyQnm0U/+fLBiBHObgJ+7+xZeOghM4SV4qabYMIE5/CWiIi4cHtS88477/DUU0+RO3fuqw4qNjaWTz75hJdeeumqr3EtlNRkr+hoyJtXIzTpWJYp5vPss87VUOXLm9tR9erZGpqIiCdye1LjC3wtqUlMTuTkuZMUDS1qdyhyNRYtgjvvhOPHzX6uXPD113DPPbaGJSLiaVRR2IedOneKbpO7Uej9Qjzy6yN2h5NpZ8/C6tV2R+FB2rQxVYcbNTL7586ZejYDB0JCgp2RiYh4patOagIDA3kwZSboJTz00EMEBQVd7dtIBsJyhrF0/1Ki46JZsHcBCUme/wX4yy9QowZ06uQcmBAgPBz+/BP69XMe++wzaNsWDhywLy4RES901UmNZVlk9s6VH93hyhYBjgBurHAjhXIVolPlTh5Zr+ZC338P+/ebhKZ/f7uj8TA5c5rbTl99BSmrCJctg/r1/Xw9vIjIlcny20+xsbEuy73FPUZ2GsmxQceY2H0iRUKL2B3OZY0Y4Vzc8+OP5iEXePhhWLIEypQx+ydOmJVRr7+u9goiIpmQpUnN6dOnWbp0KSVKlMjKt/FLBXIVIMDhPVOiihc3iU2Kxx+Ho0fti8djNWkCa9aY+3RgVkq98QZ07AjHjtkbm4iIh7ui1U8VKlRI3d63bx958uS5aL2axMREjhw5QlJSEo888giff/75tUd7jXxt9ZO3sSzo0cNZSLdbN5g6VUu+M5ScbHpFvfyy2QYoUQImT4aWLe2NTUQkm2XJku6AAOfIgMPhuOxcmRw5ctClSxdGjRpF/vz5M/s2WcZXkxrLsohLiiNnUE67Q7msY8egZk1zZwVMDbq777Y3Jo+2eLH5B0rpDBoYCEOGmBo3Ad4zUicici2yJKn5999/AfMlWqFCBXr06MEHH3yQ4XNz5MhBkSJFPGrlk68lNcfOHuPVha8yd/dcbqxwI6M6j7I7pEyZMsWUZwEzz2bzZnN7Si7iyBHo1QsWLnQeu/VWGDtWVYhFxC9kefG9vn370rJlSx544IGrDjK7+VpSE5sQS8H3ChKXFEfZsLLsfXIvDi+5l3PXXc7JwrfdBtOn6zbUJSUlmQnDb7/tPBYebtortGhhW1giItkhy4vvfffdd16V0Pii3MG5aVm2JTkCc1CxYEVi4mPsDinTRoyAIkUgd27o0MHuaLxAYKBpfPnbb1CokDkWEWEabL31llZHiYigNgleb++pvRQNLUpojlC7Q7liixaZ1ctp5p9LZkREmFYKS5Y4j7VpA+PGQalStoUlIpJV3D5Sc9ttt7Fly5ZrCmrTpk106dLlmq4hrsoXKO+VCQ2Y72ElNFchPBwWLDC3o1ImCy9aBHXqmNLNIiJ+KtNJzYIFC6hbty49e/bkjz/+yPQbWJbF77//zh133EG9evVYtGjR1cQpfiJlVZRcRlAQvPaamTxcurQ5dvKkmaA0YACcP29vfCIiNsj07afDhw/z7LPPMnHiRBwOByVLlqRdu3Zcf/31VK9enUKFCpEvXz6io6OJjIxky5YtrFixggULFnD48GEsy6JXr168//77lCxZMqv/XhnyxdtPF7Isy2smC6d15gwMHgzjx8PGjc7vacmEyEh48EGYMcN5rF49mDQJqla1LSwREXfJstVPf//9N59++inTpk0jPj7+kl+glmURHBzMHXfcwcCBA2nYsOGVvJXb+WpSc+TMEUauGsncPXPpWLEjb7R9w+6Qrtizz8JHH5ntjh1h9mythroilgVffAFPPw1xceZY7twwfDj07at/TBHxalm+pPvYsWPMnj2bBQsWsHbtWo4ePUpUVBT58+enaNGiNGjQgLZt29KpUyeKFi161X8Rd/LVpOZwzGFKfmxGvxqVbMSqh1bZHNGVO3XKFOU7fNjsjxxpWinIFdqwwRTr27rVeaxrVxg1Ci5S/VtExNNleVLjjXw1qQGo+2VdNhzdQJ1idfj7ob/JEZjD7pCu2OzZcMstZjskBFatMnNf5QqdPQsDB8I33ziPFS8O334LN99sW1giIlcry+vUzJkz52pfKllgdJfRHHz6IOsfXe+VCQ2YHo4DBpjtuDgz4BAba29MXik0FL7+2jTZSqlpc+SI+Qfu31//qCLis646qenUqRNVq1bls88+Izo62p0xyVVoWLIhJfPaMwHbnd5/38xxBXMHZeBAO6Pxcl27mlnXHTs6j40cCdddB//8Y19cIiJZ5KqTmurVq7Nz506efvppSpUqxWOPPcamTZvcGZv4oZAQs2gnd26z//XXpleUXKUSJcx9vREjIOd/DU+3bYOmTeGdd1SJWER8ylUnNZs3b2bBggV07dqVuLg4vvrqK+rWrUvbtm2ZNm0aycnJ7oxT/EjVquY7OMVDD8G+fbaF4/0cDnjiCVi7Fho0MMcSE+Hll02bhb177Y1PRMRNrjqpAWjTpg1Tp05l7969vPTSSxQtWpTFixdz5513UrZsWd555x2OHTvmrljlMo6fPc7wlcPpPLEzo/7xjo7dF9Onj5lTA+Z2VHCwndH4iGrVYMUKePFFZyXiZcvMbOxRo8yycBERL+bW1U8JCQlMnTqVESNGsGLFChwOR2qdmv79+9OkSRN3vdVV8eXVTwAbj26kzpdmuVCnyp2Y1WuWzRFdm6go+O47+N//TD9HcaNly+Dee11Hadq3h9GjTRsGEREPkuWrnzISHBxMz549Wbx4MYMHD8ayLOLj4xk/fjzNmjWjZcuWrFy50p1vKWnUKlqL4nmKA7D9xHaSLe++BRgWZiYKK6HJAs2bw7p1phJxinnzoFYtk0lq1EZEvJBbR2qOHj3KqFGjGDVqFIcOHcKyLOrXr0+HDh2YOHEi+/fvJzAwkGnTptnS2NLXR2oAZu+cTel8paldtLZXtku4nNOnzdzWlJXK4ga//Qb9+sGhQ85jnTqZWdo2tTQREUkrW4vvLV++nBEjRvDTTz+RkJBAQEAAt99+O08++SQtWrQAIDk5ma+++ooBAwZQu3Zt1qxZc61ve8X8IanxZStWQK9eZjDhl19U+d+tTp2Cp56CsWOdx/Lnh2HDoHdv/WOLiK2yPKk5f/4848ePZ+TIkaxfvx7LsihQoAAPPfQQTzzxBOEXuS/fuXNn/vjjD86dO3c1b3tNlNR4r/PnoWJF52DCZ585C/WJG82cCQ8/bIr1pbjtNvjyS1OVWETEBlk+p6ZUqVI8/PDDrFu3jho1avDVV19x4MAB3n333YsmNADFihUjPj7+at9W/FTOnOZuSIpBg8CGwT7f17kzbN4M99zjPDZjhmnM9cMPmmsjIh7tqpOa06dPc+uttzJv3jw2btzIQw89RK5cuS77uueee44FCxZc7dtKJpxLOMf0rdPpOa0nEzdOtDsct+nUydwhAYiPh+7dITLS3ph8UsGCMG6cabNQpIg5dvIk3Hef+SH8+6+98YmIXMRV337as2cPFSpUcHc8Wcpfbj+tPLCSpqObAtCxUkd+u+c3myNyn7g4aNXKNLsE6NDBFMzVCqkscvy4WVM/ebLzWGgoDB1qCvoFuHUBpYhIhrL89pO3JTT+pHGpxpQJKwPA2sNriUuMszki9wkJgWnTnAMIc+fCK6/YG5NPK1LE9K2YMQNKlTLHzp41E5patIAtW+yNT0QkDf2a5YMcDgcftv+QOffMIeKpCEKCQuwOya1Klzb9oFJGZ4YONXdKJAt16WLm2jzyiPPYihVQvz689Za5HygiYjO31qnxdP5y+8lffPqpc45NnjywY4fp3yhZbPFi05Br507nsdq14ZtvoHFj++ISEZ9lS0Vhkez05JPQsyfkyAEff6yEJtu0bg3r18PzzzuHyzZuhOuvNyWgY2JsDU9E/JdGasSrnT0L27bBddfZHYmfWrPGVCNeu9Z5rFQpU0ioWzcV7RMRt/DqkZqEhATmz5/PoEGDaNSoEfnz5yc4OJjixYvTpUsXZs3y7kaN2cWyLP468BdP//40fX7uY3c4WSI0VAmNrRo0gJUr4d13IaWkw8GD0KOHqXmzb5+t4YmIf/HIkZo//viD9u3bA1C8eHGuu+46QkND2bJlC5s2bQLg4Ycf5ssvv7yi/kb+NlJjWRYVh1Vk7+m9BDoCOfzMYYqEFrE7rCz3009mjk2HDnZH4mf27oX+/c0a+xS5csFrr8HTT0NwsH2xiYhX8+qRmoCAALp3786ff/7J4cOH+fXXX5k8eTIbN25k0qRJBAYGMmrUKH744Qe7Q/VoDoeDO2veCUCAI4C/D/1tc0RZKykJXnjBFOW7+27Ys8fuiPxM+fLw669maVpKI8xz52DwYDOis2yZvfGJiM/zyJGay+nXrx+jR4/mhhtu4I8//sj06/xtpAZg+4ntrDiwgtuq3kaBXAXsDidLJSdD166m2SVA3bqwfDnkzm1vXH4pOtoUEBoxwvxgUvTrB++9Z6oWi4hkkleP1FxO/fr1AYiIiLA5Es9XtXBV+tTr4/MJDZjitt9/D5Urm/3166FvX9fvVMkm+fKZycKrVrlOevrmG6hSxTTySkqyLz4R8UlemdTs/K8+Rgmt4ZULhIXBzz+bCcQAP/6oisO2uu46M5F42DDIm9cci4w0ncCbNnX2uxARcQOvS2qOHDnCmDFjAOjevbu9wYhHqlHDVPZPaUs0ZAh89529Mfm1wEDTP2rbNujVy3l89Wpo0sTckjp+3L74RMRneFVSk5iYSO/evYmKiqJ27do8krZkewbi4uKIjo52efirfaf38d7S92j0dSOOnDlidzhZ7tZb4ZNPnPsPPwxqDm+zkiVh/HhYtAhq1XIeHz3a3JIaMQISE20LT0S8n1clNY8++ijz58+nUKFCTJ06lRw5clzy+UOHDiUsLCz1ER4enk2Rep6v//mawfMHs/rQan7a6h+NkgYMMAMEYL4ru3c3gwVis9atTbG+zz4zc28ATp82P6yGDWHpUlvDExHv5TVJzZNPPsno0aMpUKAA8+bNo0qVKpd9zQsvvEBUVFTqw58nFqcs7QbYcHSDjZFkr08+gVtuMdvBwWZRjniAoCCTde7YAX36OI+vXw8tW0Lv3nDggG3hiYh38ool3c888wwff/wx+fPnZ968eTRs2PCqruOPS7pTWJbFF6u/oGOljlQoUMHucLLVmTNm2saQIVDBv/7q3mP5clO4L227hVy5TH+pQYO0Ll/Ez2X2+9vjk5rnnnuODz74gLCwMObNm0ejRo2u+lr+nNSIeLykJLPU+6WX4ORJ5/HSpU0bhp49nbO/RcSv+ESdmsGDB7stoRFJKzkZfv/d7ijERWAgPPoo7NplWrAHBZnjBw6Y21HNmsFff9kbo4h4NI9Nal5++WXee++91FtOSmjEXWJj4c47oWNHLfX2SAUKwKefwsaNzglRYOrdXH+9SXD8eH6ciFycR95++uWXX7jtttsAaNiwITVr1szweYULF+bDDz/M9HV1+wli4mKYvm06P27+kVur3MqjDR+1O6RsN3Gis1xKUJAZsWnXzt6Y5BJ+/x2eegq2bnUey5XLzLUZNMh0LxURn+bVc2rGjBlD3759L/u8smXLsm/fvkxfV0kNbD62mVpfmBohLcq0YEnfJTZHZI8BA2D4cLOdN68pndKgga0hyaUkJsJXX8Grr7rOtyleHN54Ax54wHm7SkR8jlfPqenTpw+WZV32cSUJjRg1i9akRpEaAOyP2s/Z+LM2R2SPTz6Bzp3NdkwM3HSTath4tKAgeOIJM99m4EBnAnPkCDzyCNSpAzNnguf9jiYi2cgjR2qyikZqjDm75pAvJB9NSzclwOGReW22iI01yUxKrbfwcLNdpoy9cUkm7NgBL74I06a5Hm/VCj74ABo3ticuEckSXj1SI1mrY6WONAtv5tcJDZjSJzNnQr16Zj8iAtq3h2PHbA1LMqNKFZg6FZYtM5OHU/z5p+kndffdsHu3ffGJiC38+1tN/F7+/GYeakqB6h07zKqoqChbw5LMatbMJDbTpkHlys7jkydD9ermVpWaZYr4DSU1QlJykt0h2KpoUZg719R4A1MuJSHB3pjkCjgc0K0bbN5smmIWKWKOJySY/lIVKsBrr6lHhogfUFLjx1YdXEWfn/tQ98u6JFvJdodjq7JlYd486NED5s+HwoXtjkiuWHCwczLxyy+bZd9g+mS8+aZJbj76CM6dszdOEckymijsx9r/0J4/9vwBwJx75nBTpZtsjkjEjQ4dgrfegm++MUvCU5QqZZaG9+1rEiER8XiaKCyX9XjDxwHInzM/h2IO2RyNZzp1yhS39Z/U34eULAlffGHW6t9zj7lNBXDwoFkGXqMGTJpkemaIiE9QUuPHOlftzPe3f8/Bpw/St/7lix36myNHoHVrU8z25ZftjkauWsWKMG4crF8PXbo4j+/aZZpkNmgAv/yizFXEByip8WNBAUHcW/decgfntjsUj7RsmWk/BDBkiLljoe89L1a7NsyYAcuXQ5s2zuPr18Ntt5naNrNm6Ycs4sWU1IhcRPfuzlYKYKZnvPKKvvO83vXXw4IFZslbw4bO46tXw623QtOmMGeOftAiXkhJjaRKTE7kcMxhu8PwKP37m1XBKd55xxSy1fedl3M4TKXFVavM6E1KBUYwx26+2dTAmTdPP2wRL6KkRohLjOPNxW9S/rPy9Pqpl93heJwBA0z5kxTvvgvPP6/vOp/gcJh5NmvWwE8/mR5SKf76Czp0gJYtzTp//cBFPJ6SGiFHYA7GbxzPgegDLNq3iK3Ht9odksd54gn4/HPn/gcfwKBB+p7zGQ4HdO0Ka9fClClQs6bz3LJlcOONpq/U77/rhy7iwZTUCA6Hg8caPkaAI4DOVTqTZPl3heGLeewx+Oor5/5HH5kVweJDAgJMBcYNG5ytFlIsXWp6aDRpotVSIh5KxfcEgOi4aE6fP02ZMLWovpxvvoGHHoLevWHMGNNWQXxUUhL8+KOZJb71ghHMOnXMWv9u3fQfgUgWy+z3t5IakauwcKG5G6HvMj+RnAzTp8Pbb8O6da7nqlUzs8d79oSgIFvCE/F1qigskoXatk2f0Bw4oOK0PisgwKzxX7MGZs40NW1SbNsG990HVavCqFFw/rx9cYr4OSU1kqENRzewM3Kn3WF4jS1bTGHa++5Th2+f5nCYWjZ//WWWe7dq5Ty3Z49pv1C+vFkiFxVlX5wifkpJjbjYc2oPLb9rSd0v6/LOknfsDscrnD1rVv4ePw7jx5sVwmfP2h2VZCmHw6yIWrzYPDp0cJ47cgReeAHKlDFr/w+r9pNIdlFSIy6K5ynOpmObAJi0aRKRsZE2R+T5QkNh5EgICTH7c+bADTdApP7p/EPKUu+//zYrp1IaZ0ZHw/vvQ7lyZmb5jh22hiniD5TUiIvcwbnpU7cPNYvU5KMOH5EzKKfdIXmF224zVffDwsz+ypWmZltEhL1xSTZq2NDUuNm2zSQxOXKY4/HxZslctWpmXs6qVfbGKeLDtPpJ0jmXcI6cQTlxpPzGKZm2fr0pZXLkiNkvXdokO2nLnYifOHzY9Nj44gszapNWixbwzDPQubOW0IlkglY/yVXLFZxLCc1VqlvXFKCtVMnsHzhgvr9WrrQ3LrFBiRJmwvD+/ebP4sWd55YuNRWMq1Uz9y41CUvELZTUiLhZhQrmO6t+fbN/8qSZU5oyeiN+JizMTBjeuxe+/tp12G7XLtM1NTzcTC4+dMi+OEV8gJIauaTI2Eg+XP4hB6IP2B2KVylWDBYtMvVsAN580/UXdfFDOXNCv36waRPMnm1mk6c4dcqM5pQrZ+oCXFjgT0QyRUmNXNTP236m1MelGDRvEF+u/tLucLxOvnzmu2v8eHjqKbujEY8REAA33wx//GGSl/vug+Bgcy4hAX74wQzztWkD06ZBYqKd0Yp4FSU1clGNSzVObW759ZqviU+Ktzki75MzJ/Tqlf743LkQF5f98YiHqVsXxo6FffvM7acCBZznFi82S8QrVID33lONAJFMUFIjF1Uyb0kebvAwjzV8jNUPrSZHYA67Q/IJs2aZFVLt28OJE3ZHIx6hZEkYMsTUABg50rRcSBERAYMHm6V0Dz1kOoiLSIa0pFsuybIsrYRyo9hYU0X/2DGzX6EC/PqrlnzLBZKTze2pYcNMFnyhNm1gwACzJFxNNMUPaEm3uIUSGvfKndskMSmThvfsgeuvN7ejRFIFBJjWC7/+aioRP/kk5M3rPL9oEXTrZjLkt95SKwaR/yipkStiWRZxiZoMci0aNTJFZevVM/tRUdCpk7nrIJJO5crw6adw8CAMHw5VqjjPHTgAr75q+kzdeadJdvxn8F0kHSU1kimWZTFrxywaf9OY1xe9bnc4Xi88HJYsMe0VAJKSTLmS/v212EUuIm9e8x/I1q3w22/m1lPKSGpiomnR0LYt1Kxpkh91CRc/pDk1kimHYw5T7rNyxCfFExocyt4n91IktIjdYXm95GSz6OX9953HOnSAyZMhf37bwhJv8e+/MGqU6S2VMlErRe7ccM898Oij0KCBPfGJuInm1IhblchbgocaPARApYKVOHJG5XHdISDArNb97jtnqZJVq0wVYpHLKlsW3nnHrJCaONF0UU0RG2sqGF93nXl8+WX6HlQiPkYjNZJpB6MPsvLgSm6vdjsBDuXD7vbnn6aJ85gxcMstdkcjXmvTJtNE84cfICbG9Vzu3HDXXfDww9CkifP2lYiHy+z3t5IaEQ8SHW0qEacVG2saOYeE2BOTeKmYGDN68/XXsHp1+vO1apm6N717Q8GC2R+fyBXQ7ScRL3ThZ9WyzPdOq1am2bNIpuXNa0Zk/v4b1qyBxx5z/Q9s0yazVLxkSZPYzJ9vJnmJeDElNXLVDsccZvrW6XaH4dO++AImTDDzbBo0UD0buUr168Pnn5su4N99B82aOc/FxZkGZTfeaKpBvvaa6Sgu4oWU1MhVeWn+S1QYVoFeP/XicIwKf2WV66839dXAtP7p2BHeflu/UMtVCg2FPn1g2TLnSE3aW0///mtayleoAO3amXk5sbG2hStypZTUyFU5n3g+9fHB8g/sDsdn1a8P//zjnDhsWfDKK6ZEiVZIyTWpWdMU9Tt0CH780XQOD0jzlbBwoekgXry4uQe6fLkK+4nH00RhuSpHzxyl1he1uL/u/TzX/DmKhha1OySflpwMQ4eahCblExseDuPGmfk2Im5x8CB8/725RbVzZ/rzlSqZ+Te9e0PFitkfn/gtrX7KgJIa9zqfeJ6cQTntDsOvzJsHPXuaW1FgVuS+8IK5YxAYaG9s4kMsy9yi+u47M4pz5kz65zRvDvfea9ozFCiQ/TGKX9HqJ8lySmiyX/v2sHYttG5t9i0Ltm1zvWsgcs0cDmjRAkaPNs0yx4yBG25wrWuzbJmpVly8OPToATNmQHy8bSGLgEZqxI0SkxMJCgiyOwy/kJRkWiuMGmXm3KjMiGSLAwfMSqnvv4ctW9KfL1TIJDi9epmkSNm2uIluP2VASU3WsCyL6dum8/TvTzP9runUL1Hf7pD8xvnzkPOCAbO//zZTH3RHQLKMZZkhwx9+MDUHLuw7BVC6NNx9t0lw6tVT9WK5JkpqMqCkJmtM3jSZu6fdDUCjko1Y8eAKAgM0wcMOR45A7dqQK5cmEUs2SUw0k72+/97cgjp3Lv1zqlUzk8F69oTKlbM/RvF6mlMj2aZr9a7UKFIDgEK5CxEdp6Z5dnnySThxwvQ3bNMGXnzR1FYTyTJBQWY5+MSJZsRm3DhTgyAoza3obdtMUb8qVaBRI/jwQ1MTR8TNNFIjbrE8YjkHow/So0YPHBpmtk1EhFmQsnix81iNGmYRS+PG9sUlfujECZg2zdye+vPPjJ/TtKlZPdWjh6lRIHIRuv2UASU14g9SJhG/+qq5MwBmvuYzz8Abb5hbUyLZKiICJk82Cc7atRk/p1kzZ4JTqlT2xiceT0lNBpTUiD/ZsAH69jW9DFNUqQLffmtKjIjYYscOmDLF1L/ZsCHj5zRvbpKbbt2gTJnsjU88kpKaDCipyT5bjm9h6NKhjLp1FLmCNTRgl8RE+OADeP11ZwmRokVh3z6N2IgH2LbNmeBs2pTxcxo1MslN9+6aZOzHvH6i8Pbt2xk+fDh9+vShdu3aBAUF4XA4ePvtt+0OTS5jzLox1PuyHuM2jGPIkiF2h+PXgoJMxeF168z0BYBhw5TQiIeoVs30/ti4ETZvNtl39equz/n7b/MfcZUqUKeOec7GjepDJRny2KTmiy++YMCAAYwdO5ZNmzaRlJRkd0iSSU1KNUndnrZ1GglJCTZGI2C+J5YuhZ9+MtMW0jp6FE6ftiUsEacaNcwKqS1bTILz5pumvk1aGzeaiWF16kDVqvD886bRptrWy388NqmpVasWzz77LOPHj2fr1q3ce++9dockmVS9SHVeavkSL7d8mX8e/ofgwGC7QxJMb6iuXdPXQHv8cfP98P33+uVXPESNGmYEZ+1a2LXL3ENNGWpMsXOnmRHfvDmUKGE6if/6a8Z1csRveM2cmj59+jB27FjeeustXn755au6hubUiLj67Tfo1Mm536oVjBwJtWrZF5PIRR04AD//bJaK//lnxiM0uXPDTTfB7bebejmFCmV3lJIFvH5OjYhkvVq1zPzLFH/+aUb8n30WYmJsC0skY6VLQ//+sHChuW/63XcmeUk7SSw2FqZPh/vvh2LFTBXKDz80k5K943d4uQZKaiRbRJ2PYsLGCXaHIRcID4epU82ITcWK5lhSEnz0kZmHM2WKvgfEQxUuDH36mATmxAnTouGBB6BIEedzkpJMJcpBg8x/0JUrw8CB8Mcf6ijuo3w6qYmLiyM6OtrlIdlv+tbpVBtZjXt+uodl+5fZHY5koGNHs6L2jTcgJMQcO3jQTCq+6SZTWkTEY+XODV26wOjRcPgwLFlihhsvXAK+ezd89hm0b2+Soh49YOzYjBtyilfy6aRm6NChhIWFpT7CVYbbFgeiD3DkzBEAXl/8ur3ByEXlzGmqEG/e7DrPZt48c0zEKwQGQosWZnLxjh2wfbsZemzb1pxLERNj5ub06QPFi5s+Iq+9Bn/9ZUZ4xCv5dFLzwgsvEBUVlfqIiIiwOyS/9Hijx7muxHXcUP4Gxncbb3c4chkVK5pFJD/9ZG5P3XyzmbYg4pWqVIGnn4YFC8xtqkmToHdvKFjQ+RzLMvVw3nwTrr/ezMXp1Qt++EGjOF4m6PJP8V4hISGEpIyli20CAwKZ2XMmRUOLEhgQePkXiO0cDrP8u0MH8wtt2mXglgUPPwy33mpG/NW/VLxG/vxw113mkZRkRmV+/RVmz3Zt2RAZabqOT5xo/gNv2NBk9zfdZEZ0gnz6q9Or+fRIjXiOEnlLKKHxQqGhZmQ+rZkz4ZtvzOhNu3auvaVEvEZgoKlxM3QorF9vlot/841pyZB2yXDaUZzmzc0S8W7d4MsvYc8e++KXDCmpEVskJCXw3tL3OBN/xu5Q5ApNn+7cXrTI/BJ7//3mO0HEa5UqBQ8+aObZnDhh/uN+/nlTvTit6GjzIXjsMXOvtlIleOIJs/pKi1Fsp6RGst2B6AO0GduGwfMH88ivj+Al9R/lP99+a/6/n7IE3LJMNeIqVWDwYDNyL+LVgoOhdWt4913nKM6338Ldd6cv5rd7N3z+uRm6LFjQjOa8+qop+qRl49lOSY1ku3MJ59h4dCMAUzZPYcvxLTZHJFfC4TCj71u2wCefQIEC5vi5c/Dee1C+vFlEEhVlb5wiblOqFPTta+bYHDtmbke9845JfNLOr0lKMr2o3nrLnCtQwNRL+PBD0/JBPaqynMe2SVizZg2PP/546v7u3bs5ceIEpUuXplSpUqnHp0+fTokSJTJ1TbVJ8BxTNk9h0LxBTO4xmSalm1z+BeKxTp6Et9827RXS/mK6ahU0amRfXCLZIibGFPibO9c8tm+/+HMLFTIT0dq1M0vMq1TRTPtMyuz3t8cmNYsWLaJt27aXfd7evXspV65cpq6ppMaznEs4R67gXJd/oniFiAjzy+vo0ablzs8/2x2RiA0OHDDLx//4A+bPh0OHLv7cEiVMG4e2bc2flSopybkIr09qsoKSGpGst2ePmWeTMucGzKj7LbeYJeAPPgg5ctgXn0i2sSwzcjN/vklyFi689H3ZUqWcCU6bNlChgpKc/yipyYCSGs82edNkTp0/xaMNH7U7FHGzSZOgZ0+zXbq0qWDfr59ZMi7iN5KSTA2EhQvN6qolS+DMJVaAlioFrVo5H9Wr+22So6QmA0pqPJNlWfzvt/8x8u+RBAUEsaTvEpqWbmp3WOJGTz0Fn37qeqxwYXjySbMaNmWysYhfSUiAf/4xCc7ChbB0qekyfjGFC0PLls4kp25d19YPPiyz399a/SS2czgchAabX9kTkxP5aetPNkck7vbJJ7ByJXTu7Dx24gS88gqULWvKgRw5Yl98IrYIDoamTU0thN9/h1OnYNkyM/O+Q4f0Q5knTpgaOU89BdddZ34buOkms9pqwQI4e9aev4cH0UiNeISEpARumXALd9a8kwfrP4jDT4dY/cHGjab8x6RJritcQ0JMQdfeve2LTcSjJCTAunWm5s2ff5rbVadOXfz5gYFQv75p6Nm8uXlkcnWwp9PtpwwoqfFslmUpmfEju3ebRsrffWeWgjscsHUrVK1qd2QiHio5GTZtMgnO4sXmdtXlhjgrVIBmzUyjzuuvh9q1vbJ3lZKaDCip8T77o/ZTLLQYIUFqTOqrDh0yt6dOnDAJTlo//ggBAaZYqxf+f1gka1kW7N1rkptly8yfWy5TzDQ01DTlTElymjY1c3U8nJKaDCip8S6bjm2iww8daF6mOZO6T1JDTD+TmGiWhe/fb+bd/O9/Zjl4/vx2RybiwU6eNFWNU5Kcv/+GuLhLv6ZKFWjSxPmoU8fj6i4oqcmAkhrvEZcYR6XhlTgQbbokvt76dV5r85rNUUl2+vVX14nFYH7J7NsXBgyAypXtiUvEq8TFmXk5K1aYx/Lll+8+GxICDRq4Jjrlytm6nFxJTQaU1HiXObvm0GViF+qXqM/sXrMplLvQ5V8kPsOyTL2yTz+F2bNdzzkc0KkTPPoo3Hyz36xqFXGPAwecSc6KFaZ2zuWabxYpYm5bNWoEDRuaP4sWzZ54UVKTISU13mf+nvk0LtWYvCF57Q5FbLR9OwwbBmPGpC/jUbu2aaSsOeYiVyllNGflStO0beVK2LXr8q8rU8Y1ybnuuiy7P6ykJgNKakS826lTZtn38OGm1xRA//5mPy3LUpIjck0iI50JTsqfJ09e/nWVK5vCUw8+6NZwVHxPfFJiciIPzHiASZsm2R2K2KBAARg0yCz4mDkTbr0VHnnE9TmRkVCzJgwdCkeP2hOniNcrVMjc2339dXP/98QJU4dh0iTT56R1a8iTJ/3rdu40v1XYRCM14jXik+K5a+pd/LztZ4ICgpjYfSI9avSwOyzxMB9/DM88Y7aDgszcm/vvNwmQhy3oEPFuSUmwY4dZYZXySLmNVbeuW98qs9/fqvwgXiM4IJgiuYsAEOgIpHie4jZHJJ5o1y5z68myzLLwX34xj4IFTVPN++83UwB0e0rkGgUGmiab1avDffeZYwkJts7c10iNeJWk5CQen/U4N1a4kTtq3mF3OOKh9uyBr7+G7783xf0uVKMGvPQS9OqV/bGJyJXTROEMKKnxbUnJSSrQJy6Sksyy8LFjTR/A8+ed50aOhMcfty82Eck8TRQWvzJp0ySafduMo2c0M1ScAgNNE+MJE0yLnK+/Nr3+QkLg7rtdn7t0KXTrZlozqNmxiHfSSI14vT///ZP2P7QnPime8vnLs7LfSoqEFrE7LPFgx46lrxv22GPw5ZdmO3du6NLFJD4dO5okSETso5Ea8RsFcxWkaKj5hrqh/A0Uzu35zdnEXhcmNJZlWuWkiI01K1dvvx2KFYM+fUzbhrS3r0TE8yipEa9Xq2gt/nrwLwY2Gcjnt3yOQ8ta5Ao5HLB2LSxYAA8/bFZKpYiKMnNyOnc2leLHjLEtTBG5DN1+Ep+2I3IH5fOXJzgw2O5QxIskJJgJxpMmwc8/Q3S089yiRabuWIqoKDOyU6JEdkcp4j90+0n83onYE7QZ04ZWY1qx59Qeu8MRLxIcbIqpjh1rqhLPmGFuQVWrZiYapzV+PJQqBc2awXvvwaZNthZUFfFrGqkRn3XHlDuYumUqAN2qd2PandNsjki8XUY9pdq3N6M6aZUpYyoZ33ILtGtnJh6LyNXTSI34vUHNBlGxQEUK5y7MiJtH2B2O+ICMpmu1aGGK+aW1f79ZSdW5s5mfc/PNMGtW9sQo4s80UiM+LSYuhh2RO7iu5HUuxxOTEwkKUJcQcZ+dO03fv1mzYPFiiI93Pf/FF/Doo879+Hg4dw7CwrI3ThFvpJEaESBvSN4ME5p2Y9vxyoJXSEhKsCky8TWVK8OTT8LcuaZT+M8/m5VUpUub8506uT5/0SLTCLlZM3jtNViyxExQFpGrp19Vxe+88+c7LNm/hCX7l7Dr1C4mdp9od0jiY/LkgdtuMw/Lgm3bzDybtObNM20cVqwwjzffNK9r0wZuuMH8WacOBOhXT5FM08dF/E7OoJwEBQQR6AhkQOMBdocjPs7hME2ML1S8uFlNldaZM6bI31NPQf36ULgwPPts9sQp4guU1Ijfeb7F8yx7YBkjOo3g+vDrXc5Fx0WTbCXbFJn4k2eega1bISICvvvOdAy/sNLxqVNmNOdCX3wBq1bpdpXIhTRRWCSNbpO7cSjmEMNvHk6jUo3sDkf8jGXBxo2wcKGZbPznn/DNN6ZdQ4qICOetrFy5oHFjaN7czM25/nrXasgiviKz399KakT+M3/PfG784UYASuYtyZ4BewgJUidDsU9ysnkEpZn9OG4c3HvvxV9TvbpJcJo1M6M/OXNmfZwiWU2rn0SuUM6gnNQoYgqODGk3RAmN2C4gwDWhAdOi4fPPoWdPKFs2/Wu2boXRo+F//0v/2h074PDhrItXxG4aqRFJIyEpgcmbJ9Ordi8CHM6c/0TsCX7c/CN96/UlV3AuGyMUcXXwICxfbh7LlpnGnImJ0LatadCZVqdO8NtvZpl548bm0agRXHed6uWIZ9PtpwwoqZGr9drC13jzzzcpFlqMcd3GcWOFG+0OSSRDsbGwerXZbtXKedyyTJfxyMiMX1ehAjRoYFZd3X57+irJInbK7Pe36tSIXMa5hHMMXzUcgMhzkVQpVMXmiEQuLndu12QmRVwc9OtnVk2tXg0xMa7n9+wxj6lTzUTktElNZKSZtFynDpQvr9o54rmU1IhcRq7gXMy/bz7vLnuXvDnyUibMtYra+iPrKZirIOFh4TZFKHJ5OXPCu++a7aQk2L4d/v7bJDlr1sD69aZtA5jRmrSWLoVu3cx2aCjUqgW1a5skp04ds61VV+IJdPtJ5AokW8kuc20sy6Lp6KasObyGXrV78XXnr8kRmMPGCEWuTmKimUi8Zg3cfbfrJOPXX4c33rj060uVMs09J03K0jDFT+n2k0gWSJvQACzct5BVB1cBsP3EdiU04rWCgswtp4zm0nToYObkbNhgHnv2pH/OwYOmhs6FeveGY8ec165RA6pWNdWSM+p6LnItlNSIXIM6xerwSqtXGLFqBP0a9Et3fuiSodQqWoubK9+sruDitVLq3qSIiYHNm02Cs3GjM9mpWTP9axcuhEOHTK+rtAoUMMlN1apQpYomJ4t76PaTiBucSziHw+EgZ5Cz0tnhmMOEfxJOkpVEo5KNWPXQKhsjFMlalgXnz5sqxyliY82k44utuEpr/HhTLDDFnj3wwQdQqZLzUaGC6/XFf+j2k0g2yqh2zaRNk0iyTOOeDhU7pDu/7/Q+yoaVxaExePEBDkf6hCN3bjh+3Dw2b4YtW0xxwO3bzSPt7aqqVV1fu2EDfPll+vcpVco1ySlf3swB0sdIQEmNSJb5X5P/UblQZUavHc0D9R9wOXc2/izVR1anRJ4S9GvQjxdbvmhTlCJZy+EwjTqLFjUFAdM6exZ27TIJzoUdy3fvzvh6Bw+ax+LFZr9QIVNdOa2RI03yVL68eZQpYx5Fiij58XVKakSySFBAELdWuZVbq9ya7tycXXM4n3ievaf3sj9qf7rz8UnxmnQsPi80FOrWNY8LPfigadS5a5d57N7t3D5xwvm8cuXSv3bGjPRzeMAsa09JcMqUgS5d4Lbb3PbXEQ+gpEbEBmE5w7ixwo0s2reIrtW6upxLSEqg+IfFqVGkBt2rd+ep65+yKUoR++TPD02bmseFoqJMkrN3LwQHpz+/d2/G1zx/3ixb37HD7Jcu7ZrUnD9vbm+VLm0eabdLl4aSJc2jQAGN+HgqJTUiNrixwo3cWOFGTp07RZ4ceVzOrT60mlPnT7EsYlm6Qn8Ae07tITxfOMGBGfzfXMQPhIWZlg4NGmR8fskSM9F4717491/z2L/fuR0ba55X5oKP18GDcPKkeWzYcPH3DwkxhQtr13Ye27rVHCte3PkoVAgCA6/t7ypXRkmNiI0K5CqQ7tjp86epWqgq2yO30658O5dzlmXRdmxbTp47SYeKHZh257TsClXEa6QkFWmXoaewLDh1yiQ3pUq5nouONnNwDhyAhISLXz8uzszPSWvOHHj6addjgYHmeWkTnerV4bnnXJ93+rS5FZfRqJNcGSU1Ih7m5so3c3PlmzkYfZDQHKEu5/ac2pM6B+dM/Jl0r/1y9ZdExkbSqFQj2pRro3k5IhdwOExLh4zaOtSvb0Z4kpPNvJ0DB1wfhw+bmjtHjqRPag4dSn+9pCTz3CNHnMcaN06f1HTpYkaXChZ0TqouUsQUKEx5FCliuqlfOKFaXCmpEfFQpfKVSncsMTmRnrV68ue/f9KoZKN050f9M4q1R9YS4AgganCUS1Kz7/Q+os5HUbVwVZd6OiLiKiDAmVxc7BbXhe64A8LD4ehRk8Sk/JmynZhonle8ePrXHjtm/ky59bVtW8bvMXQoDB7s3D9xwkyyLlTIPAoWTL9dsKCZA9SokVli7+uU1Ih4kaqFqzKh+wTAJDhpnUs4x4ajZiJAjSI10s3V+WbNN7yz5B0CHAH83vt3bqxwY+q5+KR4YhNiyZ8zf9b+BUR8VOPG5pGR5GRzy+vIkYzn2DRqZBKPY8fM40z6QVjAjNikdeKEGSHKaJToQtu3m8rNKcaPh7feMu+b8ggLMxO00z6KFYPWrS9/fU+hpEbES13YdiFnUE62PLGFVQdXpetRBbDp2CbANOWsUKCCy7m/DvxF6zGtKZSrEC+2fJGnr3edHBAZG0mBXAUyvK6IXFpAgHMEJSM//OC6HxtrEpYLHxfOETp/3qzGiow083wupcAF0/cOHDCJzuVUr26KJqbVpQssXw758plEKCzMuf3NN2YitV08PqmZMmUKI0eOZP369cTHx1OpUiXuuecennrqKYI1q0oklcPhoEqhKlQpVCXD87dWuZV8IfnYeXIn5fKXczm36+QuACLPRRIc4Pq5siyLcp+VIz4pnnbl2/HbPb+5nN9yfAsJSQmEh4VTIGcBVUgWuUa5cztr6VxKvXpmxZZlwblzJrk5edL8mXb71Ckz6pJWcjLkzWv6eF3Kha8DUyE65T3Scjhg7NjL/OWymEcnNQMHDuSzzz4jKCiIdu3akSdPHhYsWMDzzz/PzJkzmTt3LrnUCEQkU/o16Jdh002A/Dnz06ZcG3af3E3lQpVdzh07eyzDSckpXln4Cj9t/QmAA08dcJkLtOHoBqZsnkLxPMVpW74tNYqoY6GIuzkcJhHKndvM68mMF14wj8REs/rq9GlT/ydlO2X/wlteYFaNVaxozkdFOVeK5c1rRqXs5LFJzc8//8xnn31Gnjx5WLx4MQ3+m6114sQJ2rVrx9KlS3nllVf48MMPbY5UxPt1q96NbtW7ZXguNiGWTpU7EREVQY3C6ZOSiChnA5+ioUVdzv198G/eXvI2AF/e8qVLUpOYnEixD4tRKFch2pRrw6jOo1xeO3f3XI6dPUb+nPm5scKNmtwskgWCgpwrrDJr6lTX/fPnzXL4s2fdG9vV8NikZsiQIQAMHjw4NaEBKFy4MJ9//jktW7ZkxIgRvPLKK4SFhdkVpojPK1+gPLN6zbro+btr3U2torWIjotOVxDwyBnnWtbieVyXfZw8dzL1UbXwBd0MgU//+pTfdplbXScGnXBJaqZumcpDMx8ib468vN3ube6re5/Lawf8NoDcwbmpUqhKur5bm45t4tS5U4TmCKVmkZqEBDknAFiWpdtnIlcoZ07z8AQemdQcPHiQv//+G4BeaXvR/6dFixaEh4cTERHB7Nmz6XlhNzMRyTYXTipO676699GwZEOOnDlCw5INXc6djT9LxQIVORF7gsK50/+aePr86dTtsJyuv7icPHeS0+dPc/r8aRKSXKukxSXGMXzVcABalW2VLql5c/GbTNkyBYB9T+6jbP6yqed+3fErXSd3JVdwLt5o80a6v1vHcR1JTE6kcsHKfHHrFy7npm6ZysoDKwkODOZ/jf9HibwlUs8dOXOEX3f8So7AHNQuWpv6Jeq7vHZFxAoSkxPJFZwr3b/TyXMniTofRVBAEEVDi7okYclWMvFJ8QQ6AgkKCFJCJn7PI5OatWvXAlCwYEHKly+f4XMaNmxIREQEa9euVVIj4qHCw8IJD8v4Jn/5AuXZNcBMULYsK935wS0G8+/pfzmbcDbdSq+QwBCqFKpCTFwMBXO5VlGLiXfOfAwNdi1eCOZ2Wur5C4obnks8R5KVxJn4MxnGtHDfQuKT4jkReyLduTm75jB67WgAetXu5ZLUbD+xnYdmPgTAc82eS5fU3DX1LiKiIyiRpwSHnnFdn/vh8g8ZunQoAAvuW0Db8s5W11uPb6XWF7UAeKDeA4y+bbTLa1t914qNxzaSMygnh5857HJu9JrRvLPkHQIDAhnWcRg3V7459dypc6do9307AhwBtC7bmo9v+tjltc/OfZbVh1bjcDiY1WsWuYOdBVDm75nPRys+IsARwOONHqdT5U6p5yzL4s6pd+LAQdVCVXmr3Vsu1/3i7y9YfmA5Dhx82OFDl9uZG49u5LOVnwFwW9Xb6Fy1s8trB80dxNmEsxQLLcZrbV5zOffT1p9YvG8xDoeDgU0HukyUj4iKSL1u8/DmdK3u2ovtw+UfcvzscXIF5+L1Nq+7nFu4dyF/7PkDgHvr3ku1ws7KeKfPn+aj5R8BULtYbe6seafLa79d+21qIc1XWr1CYIBzrfeaw2v4dcevAHSp2oV6xeulnktISuDdpe8CUC5/Oe6te6/Ldadumcr2E2ZZ04AmA8gbkjf13PYT25m21VQhb1uuLdeHX5/u75qQlECR0CLp5t/N2TWHdUfWAdC3Xl+K5SmWeu5A9AHGbRhHgCOA55pfUFkwm3lkUrP3v25kZS4x9Tv8v9lQey/WuQyIi4sjLs06t+joaDdFKCLulNEIQ5eqXS76/Pvr3c/99e7P8FxYSBh/P/Q3MXExLv9DT3FHjTuoXrg6sQmx6Wr55M2Rl+tKXMe5xHMu/9MG84UcnxQP4DJakiIuyfn/mgsrOae8DsiwZ1dCcsJFz6WtR3RhcpdkJaVup/1STBEVF8Xp86cznI906vwp9p42//9Mm+ilxJvyBRaeL31Suu7IOhb/uxgwo0VpHYg+kHrb8JbKt7ics7CYusVMyGgW3oy3cE1qluxfwsRNEwF4vc3rLklNRHREatJYJqxMuqRm9NrRnDp/isoFK6dLahbvW8ywVcMA6Fmrp0tSc+TMET5aYZKPuMS4dEnNN2u+YXvkdvLnzJ8uqVkWsYwhS81UievDr3dJaqLOR6XOJ7ur5l3pkprv1n3H0v1LAXip5UsE4vz5rT60mtcWmb9DeL5w16QmOYFXF70KmMTkwqRm4qaJqRP3+9bv6/IZ2HJ8Cy8teAmAd294N11S8/qi1zmbcJZaRWulS2p+3vYzX/3zFQA3V7rZ5fPx7+l/eWH+CwQFBCmpyUjMf2vMQkPT/5aVIk8e8z+jSyUqQ4cO5Y033nBvcCLi0YIDg9PdwknrYskQOFtUXEz8y/HEJcWl+yIHeLXVqzxy3SPEJ8VTOl9pl3PVi1Tn685fE58UT4MS6UvU9m/Un6i4KPKF5Et3rm6xutxd624SkxMpEupamz93cG5al21NkpVE5YKV0722XP5yxCXGZdguI2dQTorkLkKSlZQuSUu2kskRmINkKzldIgUmOUnhwHHxcxckq2n/3S583WWva138XFqXuwV3qfPXcvvuUjFJ9nFYGY2x2mzIkCG89NJLNG/enKVLl2b4nJdeeokhQ4bQoUMHfv/99wyfk9FITXh4OFFRUeTLl/5/HiIicnkJSQkkWUlYlkXOoJwuyUBcYpy5fYdFaHAouYKdZTcsy+JgzEEsyyI4MDjd5PEjZ44QExeDhUX5/OVdRq5i4mL4N+pfLMuiaGjRdCNpG45uIDE5kZDAEGoWrely7t/T/6ZOWq9ZtKbLCF1MXExqJe4SeUukK0z598G/iU2IJTAgkBZlWric23d6H3tO7QGgTrE6LnPDziWcY1nEMgCKhRajdrHaLq9deWBl6ryx9hXbuxS23B+1n83HNgPm1lXaJDkpOYnfd5vvvIK5CtK0dFOX664+tDr173rhqsHDMYdZfWg1YBLtSgUrubx21o5ZJFlJ5M2R1+U2J8D6I+vZd3ofAG3KtXGZ5xYZG8nS/UtxOByXHGG9FtHR0YSFhV32+9sjk5rhw4czYMAA6tWrlzq/5kJPPvkkw4YNo0ePHkyZMiVT183sP4qIiIh4jsx+f3tkzfNy5coBEBERcdHnpJxLea6IiIj4N49MaurXNysDIiMjLzoRePVqM4TWILMtVEVERMSneWRSU7p0aRo1agTAhAkT0p1funQpERERhISE0KlTp3TnRURExP94ZFID8OKLLwLw7rvvsmbNmtTjkZGRPP744wD0799f1YRFREQE8NCJwilSJgMHBwdzww03EBoayvz58zl9+jTNmzdn3rx5V9TQUhOFRUREvI9Xr35K68cff2TkyJGsW7eOhIQEKlasSO/evXnqqafIkSN97YVLUVIjIiLifXwmqXEnJTUiIiLex6uXdIuIiIhcKSU1IiIi4hOU1IiIiIhPUFIjIiIiPkFJjYiIiPgEJTUiIiLiE4LsDiA7paxej46OtjkSERERyayU7+3LVaHxq6QmJiYGgPDwcJsjERERkSsVExNzyfZIflV8Lzk5mUOHDpE3b14cDofbrhsdHU14eDgREREq6uel9DP0fvoZejf9/LxfVv4MLcsiJiaGkiVLEhBw8ZkzfjVSExAQQOnSpbPs+vny5dOH0cvpZ+j99DP0bvr5eb+s+hlmpoG1JgqLiIiIT1BSIyIiIj5BSY0bhISE8NprrxESEmJ3KHKV9DP0fvoZejf9/LyfJ/wM/WqisIiIiPgujdSIiIiIT1BSIyIiIj5BSY2IiIj4BCU112DKlCm0adOGAgUKEBoaSt26dXn//fdJSEiwOzS5jD59+uBwOC75OH/+vN1h+r3t27czfPhw+vTpQ+3atQkKCsLhcPD2229f9rV//PEHnTp1onDhwuTKlYtq1arx0ksvcebMmWyIXFJczc/w9ddfv+znc9u2bdn4t/BPCQkJzJ8/n0GDBtGoUSPy589PcHAwxYsXp0uXLsyaNeuSr7fjM+hXxffcaeDAgXz22WcEBQXRrl078uTJw4IFC3j++eeZOXMmc+fOJVeuXHaHKZfRvHlzKlWqlOG5wMDAbI5GLvTFF1/w2WefXfHrPvnkE55++mkcDgctW7akWLFiLFmyhCFDhjBt2jSWLl1K4cKFsyBiudDV/gwB6tatS7169TI8l5lCbHJtFi9eTPv27QEoXrw4LVq0IDQ0lC1btjBz5kxmzpzJww8/zJdffpmuSr9tn0FLrtj06dMtwMqTJ4/1zz//pB4/fvy4Vbt2bQuwnnnmGRsjlMu5//77LcD67rvv7A5FLuHrr7+2nn32WWv8+PHW1q1brXvvvdcCrLfeeuuir1mzZo3lcDiswMBAa/bs2anHz549a91www0WYHXv3j07whfr6n6Gr732mgVYr732WvYFKunMnz/f6t69u/Xnn3+mOzdp0iQrMDDQAqyxY8e6nLPzM6ik5io0atTIAqy333473bklS5ZYgBUSEmKdPn3ahugkM5TUeKeUn9ulvhDvuOMOC7D69euX7ty+ffusgIAAC7C2bt2alaHKRWTmZ6ikxjs8+OCDFmDdcMMNLsft/AxqTs0VOnjwIH///TcAvXr1Sne+RYsWhIeHExcXx+zZs7M7PBG/Fh8fn3qfP6PPZ9myZWnevDkA06dPz9bYRHxN/fr1AYiIiEg9ZvdnUHNqrtDatWsBKFiwIOXLl8/wOQ0bNiQiIoK1a9fSs2fP7AxPrtDChQvZuHEjMTExFCpUiMaNG9OpUydVNfVSO3bsIDY2FjCfw4w0bNiQJUuWpH6WxXOtWbOGwYMHc/LkScLCwqhfvz6dO3cmb968docmwM6dOwEoUaJE6jG7P4NKaq7Q3r17AShTpsxFnxMeHu7yXPFc33//fbpjJUqU4Ntvv6Vjx442RCTXIuUzlz9//ot+8enz6T1SJqOmFRYWxrBhw7jvvvtsikoAjhw5wpgxYwDo3r176nG7P4O6/XSFYmJiAAgNDb3oc/LkyQNAdHR0tsQkV65u3bp89tlnbNq0iejoaI4ePcrcuXNp1qwZhw8fpkuXLixatMjuMOUK6fPpGypWrMiQIUNYu3YtJ0+e5OTJkyxdupRbb72VqKgo7r//fsaPH293mH4rMTGR3r17ExUVRe3atXnkkUdSz9n9GdRIjfilp556ymU/b968tG/fnhtvvJGuXbsyY8YMBg4cyLp16+wJUMSP3XvvvemONW/enJkzZzJgwACGDx/OU089xR133EGOHDlsiNC/Pfroo8yfP59ChQoxdepUj/oZaKTmCqUMp509e/aiz0kpLJQvX75siUncx+Fw8MYbbwCwfv16lwlw4vn0+fR9r7/+OoGBgRw/fpyVK1faHY7fefLJJxk9ejQFChRg3rx5VKlSxeW83Z9BJTVXqFy5cgCX/LJLOZfyXPEu1atXT90+cOCAjZHIlUr5zJ0+fTp1GPxC+nx6t4IFC1K0aFFAn8/s9swzzzBs2DDy58/P3LlzU1c/pWX3Z1BJzRVK+SFGRkZedJLT6tWrAWjQoEG2xSXuExkZmbqtVRbepWrVquTOnRtwfg4vpM+nd0tKSiIqKgrQ5zM7Pffcc3z88ceEhYUxd+7ci65ssvszqKTmCpUuXZpGjRoBMGHChHTnly5dSkREBCEhIXTq1Cm7wxM3mDRpEmCGRqtWrWpzNHIlcuTIwS233AJk/Pn8999/Wb58OQBdu3bN1tjEPX755RdiY2NxOBwX/WIV9xo8eDAffPABYWFhzJs3L/U7MCN2fwaV1FyFF198EYB3332XNWvWpB6PjIzk8ccfB6B///7qTeKh1q1bxy+//EJiYqLL8eTkZEaPHp368x0wYADBwcF2hCjXYPDgwTgcDr777jvmzJmTejw2NpYHH3yQpKQkunfvTrVq1WyMUi5m//79jBs3LsOGsj///DP9+vUD4J577qF48eLZHZ7fefnll3nvvffInz//ZROaFHZ+Bh2WZVluv6ofePLJJxk2bBjBwcHccMMNhIaGMn/+fE6fPk3z5s2ZN2+eGlp6qJ9//pmuXbtSoEABGjRoQLFixTh9+jSbNm1i//79APTs2ZPvv/+eoCAtELTTmjVrUn9RANi9ezcnTpygdOnSlCpVKvX49OnTXQqApW2m17p1a4oWLcqSJUs4fPgwVatWVUPLbHSlP8N169ZRv3598uTJQ/369SlVqhTnzp1jy5YtqcXe2rZtyy+//JK6NFiyxi+//MJtt90GmIJ5NWvWzPB5hQsX5sMPP3Q5Zttn0O2NF/zI5MmTrVatWln58uWzcuXKZdWqVct69913rbi4OLtDk0vYs2ePNXDgQKtFixZWqVKlrJw5c1ohISFWmTJlrB49elizZs2yO0T5z8KFCy3gso+9e/eme+28efOsjh07WgULFrRCQkKsypUrWy+88IIVHR2d/X8RP3alP8MTJ05Yzz//vNWuXTurTJkyVmhoqBUcHGyVKFHCuvXWW60JEyZYSUlJ9v6l/MR3332XqZ9d2bJlM3y9HZ9BjdSIiIiIT9CcGhEREfEJSmpERETEJyipEREREZ+gpEZERER8gpIaERER8QlKakRERMQnKKkRERERn6CkRkRERHyCkhoRERHxCUpqRMRj7Nu3D4fDQbly5ewORUS8kJIaEclW5cqVw+FwsG/fPrtDEREfoxbEIuIxSpUqxdatWwkODrY7FBHxQkpqRMRjBAcHU61aNbvDEBEvpdtPIpItxowZg8Ph4N9//wWgfPnyOByO1MeiRYsuOacm5XkA48aNo3HjxuTJk4ciRYrQs2dP9u/fD4BlWYwYMYJ69eoRGhpK4cKF6dOnD8eOHbtobDt27OCRRx6hYsWK5MyZk7CwMFq1asW4cePc/w8hIlnGYVmWZXcQIuL7li5dyjfffMPUqVM5e/Ys3bt3J0+ePKnnBw8eTM6cOSlfvjxly5ZNN+cmJaEZPHgwH374Ia1ataJgwYKsWrWK/fv3Ex4ezvr163n00Uf55ZdfaNOmDbly5WLZsmUcO3aMOnXq8Pfff5MjRw6X606ZMoX77ruP8+fPU61aNapXr05UVBQrV67k7Nmz9O3bl2+//TbL/31ExA0sEZFsVLZsWQuw9u7dm+7c3r17LcAqW7ZsunOABViFChWy1q1bl3o8NjbWatGihQVYtWvXtipWrGjt27cv9fzx48etSpUqWYA1btw4l2tu2LDBCgkJsXLmzGlNmzbN5dy+ffus2rVrW4A1duzYa/tLi0i20O0nEfEqb775JnXr1k3dz5UrF08//TQAGzduZNiwYZQtWzb1fOHChXnssccAmD9/vsu13nnnHeLi4nj77bfp1q2by7myZcsyevRoAIYNG5YlfxcRcS8lNSLiVTp16pTuWOXKlQEICgqiQ4cOFz1/6NCh1GPJycn89ttvANx1110ZvlfDhg3JkycPa9eu5fz589ccu4hkLSU1IuJVypQpk+5YytycEiVKEBSUflFn3rx5AVwSk8jISKKjowEIDw93mbSc8ggICODMmTMkJycTGRmZFX8dEXEjLekWEa8SEHDx38Uude5CycnJqdv333//ZZ8fEhKS6WuLiD2U1IiIXypcuDC5cuXi3LlzfPjhhxQuXNjukETkGun2k4hkq5Ql1YmJibbGERgYSPv27QH48ccfbY1FRNxDSY2IZKvSpUsDsHnzZpsjgddee40cOXIwaNAgxo4d63JLKsWmTZv46aefbIhORK6UkhoRyVbdu3cHoHfv3nTv3p1+/frRr18/tm/fnu2xNGjQILVqcJ8+fShbtiw33XQTvXv3plOnToSHh1O7dm2N5Ih4Cc2pEZFs9dhjjxETE8O4ceOYPXt26oqk3r17Z9geIavdcccdNGrUiGHDhjFv3jyWLVtGUlISxYoVo1KlSvTv358ePXpke1wicuXUJkFERER8gm4/iYiIiE9QUiMiIiI+QUmNiIiI+AQlNSIiIuITlNSIiIiIT1BSIyIiIj5BSY2IiIj4BCU1IiIi4hOU1IiIiIhPUFIjIiIiPkFJjYiIiPgEJTUiIiLiE/4PvNtYXl74B8EAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "# function that returns dy/dt\n",
    "def model(y,t,k):\n",
    "    dydt = -k * y\n",
    "    return dydt\n",
    "# initial condition\n",
    "y0 = 5\n",
    "# time points\n",
    "t = np.linspace(0,20)\n",
    "# solve ODEs\n",
    "k = 0.1\n",
    "y1 = odeint(model,y0,t,args=(k,))\n",
    "k = 0.2\n",
    "y2 = odeint(model,y0,t,args=(k,))\n",
    "k = 0.5\n",
    "y3 = odeint(model,y0,t,args=(k,))\n",
    "# plot results\n",
    "plt.plot(t,y1,'r-',linewidth=2,label='k=0.1')\n",
    "plt.plot(t,y2,'b--',linewidth=2,label='k=0.2')\n",
    "plt.plot(t,y3,'g:',linewidth=2,label='k=0.5')\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('y(t)')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Croissance de population logistique ( Ressources limitées)\n",
    "--------------------------------------------------------------------------------------------------\n",
    "\n",
    "L'équation différentielle de l'équation logistique de Verhulst( Source Wikipédia):\n",
    "\n",
    " $$ y' = ry (1- \\frac{y}{K})   $$ \n",
    "\n",
    " $$ t(0) = 100 , t ∈ [0, 40] $$\n",
    " \n",
    "où\n",
    "- y' qui est l'évolution de la population en fonction du temps t\n",
    "- y qui est la fonction\n",
    "- r qui est le taux de croissance\n",
    "- K le seuil de population, ou la capacité de charge, c'est pour cela qu'on dit \" Ressources limitées\"\n",
    "- t(0) qui est la population au temps 0\n",
    "- [0,40] qui est le nombre de pas de temps, autrement dit l'étendue de l'analyse.\n",
    " \n",
    "qui est généralement utilisé pour modéliser la croissance auto-limitée d’une population biologique, c’est-à-dire une croissance limitée par des ressources limitées.\n",
    "Initialement, la croissance suit un modèle approximativement exponentiel avec un taux de croissance r.\n",
    "À mesure que la taille de la population se rapproche de la capacité de charge K, la population\n",
    "La courbe s'aplatit, pour un modèle généralement utilisé pour modéliser la croissance auto-limitée d'une population biologique.\n",
    "\n",
    "Source : Simula Springer Briefs on Computing 15\n",
    "Joakim Sundnes\n",
    "Solving Ordinary\n",
    "Differential Equations in\n",
    "Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution graphique\n",
    "\n",
    "La solution d'une eq diff étant une fonction, on dessine une fonction...\n",
    "\n",
    "On prends garde à bien respecter la nomenclature des noms des variables et des fonctions, pour que cela corresponde au modèle mathématique, comme en recherche opérationnelle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2067,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Taux de croissance\n",
    "r = 0.2\n",
    "# Seuil de population\n",
    "K = 200\n",
    "\n",
    "# Equation\n",
    "def deriv (y,x) :\n",
    "    return y * r * ( 1 - (y / K)) # On recopie bêtement l'équation différentielle citée plus haut, tirée de Wikipédia\n",
    "\n",
    "#  Time points\n",
    "x = np.linspace ( 0 , 40) # C'est l'étendue de notre analyse\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 100 # Au début, il y a 100 individus\n",
    "\n",
    "# Résoudre l'équation diff\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Individus\" )\n",
    "plt.ylabel(\"nombre\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Symbolique\n",
    "\n",
    "A venir !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appliquer directement la fonction logistique\n",
    "\n",
    "basé sur cette vidéo \n",
    "https://www.youtube.com/watch?v=TfgqscbJZ1s\n",
    "\n",
    "\n",
    "<img src=\"img/verhulst.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2068,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x24041886310>]"
      ]
     },
     "execution_count": 2068,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s = 100 # seuil maximum de population\n",
    "k = 0.1 # Coefficient de croissance de la population\n",
    "t0 = 60 # Temps du point d'inflexion\n",
    "\n",
    "# On définie les dimensions du graphique\n",
    "t = np.linspace(0, 140, 100)\n",
    "\n",
    "# On écrit la fonction directement comme dans le document\n",
    "fonction = s  / (1 + np.exp(-k * (t - t0)))\n",
    "\n",
    "# On trace l'équation logistique\n",
    "plt.plot(t,fonction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <b>Cas Pratique 3 : Loi de Réchauffement/Refroidissement de Newton</b>\n",
    "--------------------------------------------------------------------------------------------------------\n",
    "\n",
    "On visionne déjà une bonne intro en Anglais sur Youtube, ou il a les idées particulièrement claires  :\n",
    "\n",
    "Source:  \n",
    "\n",
    "https://www.youtube.com/watch?v=h7QuYsrlOFY&list=PLX2gX-ftPVXV10J9jL1Lb46pPQVgBbL4Q&index=6\n",
    "\n",
    "Le réchauffement ou le refroidissement d'un objet se fait plus ou moins vite en fonction du temps et de la température ambiante.\n",
    "La loi de refroidissement de Newton stipule que le taux d’évolution de la température d’un corps est\n",
    "proportionnel à la différence entre la température de ce corps et celle du milieu environnant.\n",
    "\n",
    "Version de Michel Van Biezen ( Refroidissement ) :\n",
    "$$\n",
    "\\frac{dT}{dt}\n",
    "= -k(T(t) - T(b))\n",
    "$$\n",
    "\n",
    "où\n",
    "- T est la température\n",
    "- dt est le temps\n",
    "- dT / dt est le changement de la température en fonction du temps ( respect to time in english)\n",
    "- k est une constante ( taux (rate))\n",
    "- T(t) est la température au temps t et T(b) la température de l'environnement\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "## Exemple 1 : Température d'un thé en fonction du temps\n",
    "--------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "La température d'un verre de thé glacé est initialement de 5∘. Au bout de 5 minutes, le thé s'est réchauffé à 10∘ dans une pièce où la température de l'air est de 30∘.\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/the.jpg\">\n",
    "</div>\n",
    "\n",
    "- Déterminez la température en fonction du temps.\n",
    "- Quelle est la température après 10 minutes ?\n",
    "- Déterminez quand le thé atteindra une température de 20∘.\n",
    "\n",
    "Source : https://personal.math.ubc.ca/~CLP/CLP1/clp_1_dc/sec_newtonCooling.html\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notons T(t) la température du thé t minutes après sa sortie du réfrigérateur, et soit A=30\n",
    "la température ambiante.\n",
    "\n",
    "Par la loi du refroidissement de Newton,\n",
    "\n",
    "$$\n",
    "\\frac{dT}{dt}\n",
    "= K(T - A)\n",
    "$$\n",
    "\n",
    "Ou \n",
    "- dt est le temps\n",
    "- dT / dt est le changement de la température en fonction du temps ( respect to time in english)\n",
    "- K est une constante\n",
    "- T est la température au temps t minutes après être chauffé\n",
    "- A est la température de l'environnement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Graphique\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2069,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "K = 0.044629 # Taux de refroidissement qu'on ne peut trouver qu'après un calcul mathématique - voir partie après\n",
    "T = 5 # Température de l'objet\n",
    "A = 30 # Témpérature ambiante\n",
    "\n",
    "# Equation\n",
    "def deriv (y,x) :\n",
    "    return - K * ( T - A )\n",
    "\n",
    "#  Time points\n",
    "x = np.linspace ( 0 , 60)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = T\n",
    "\n",
    "# Résoudre l'équation diff\n",
    "solution = odeint ( deriv , T , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Température\" )\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## Solution Numérique\n",
    "\n",
    "On remplace les valeurs lues dans l'énoncé du problème du thé dans l'eq diff de NewTon, ça donne\n",
    "\n",
    "$$\n",
    "\\frac{dT}{dt}\n",
    "= K(T - 30)\n",
    "$$\n",
    "\n",
    "Avec K qui est une constante qu'on ne connait pas encore mais qu'on va calculer ensuite.\n",
    "Le problème, est qu'on ne connait pas cette valeur K, du coup, on ne connait pas l'équation \n",
    "de la température en fonction du temps, mais comme on a des informations dans l'énoncé, on va pouvoir \n",
    "trouver la valeur de K par déduction.\n",
    "Pour cela, on utilise ce processus :\n",
    "\n",
    "On utilise d'abord leur corollaire :\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/crol.png\">\n",
    "</div>\n",
    "\n",
    "On trouve T(t)\n",
    "\\begin{gather*}\n",
    "T(t) = [T(0)-30]\\,e^{Kt} + 30\n",
    "=30-25 e^{Kt}\n",
    "\\end{gather*}\n",
    "\n",
    "\n",
    "Ensuite, on cherche K, pour cela on se sert des données de l'énoncé qui disent que t(5) = 10 ( Ce qui veut dire qu'au temps 5, la température du thé est de 10 degrés), On note qu'Il s'agit d'un cas de <b>réchauffement</b>, pas de <b>refroidissement</b>.\n",
    "Donc, on remplace chaque valeur dans l'équation pour trouver l'inconnue constante nommée K\n",
    "On a donc une equation a une inconnue à résoudre :\n",
    "\n",
    "\\begin{gather*}\n",
    "T(5) = 30-25 e^{K * 5} = 10\n",
    "\\end{gather*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2070,
   "metadata": {},
   "outputs": [],
   "source": [
    "# T5 = 30 - 25 ⅇ  ( 5 * K ) = 10\n",
    "\n",
    "# Déroulé du calcul à la main\n",
    "# 25 ⅇ  ( 5 * K ) = 10 - 30\n",
    "# 25 ⅇ  ( 5 * K ) = -20\n",
    "# ⅇ  ( 5 * K ) = 20 / 25\n",
    "# 5 * K = log(20/25)\n",
    "# K = 1/5log * 4/5 \n",
    "# K = - 0.044629\n",
    "\n",
    "# Le but va être de réaliser ce calcul précédent avec Python et/ou directement SYMPY (A venir)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Désormais, on a trouvé la constante K, du coup, on obtient l'équation permettant de trouver la température au temps t choisi.\n",
    " Vu que dans l'énoncé, on nous demande la température du thé pour t = 10 , on substitue toutes les valeurs dans l'équation originelle, afin de simplement trouver la température du thé au temps t = 10.\n",
    " On vérifie qu'on trouve bien pareil que dans l'exercice, oui, c'est pareil."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2071,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " La température de mon thé au bout de 10 minutes sera de  14.00004635787813  degrés\n"
     ]
    }
   ],
   "source": [
    "# T(10)= 30 − 25 e 10*K\n",
    "# Donc\n",
    "# T(10) = 30 - 25 e 10 * -0.044629\n",
    "\n",
    "# Calcul avec python :\n",
    "import math \n",
    "temperatureApres10 = 30 - 25 * math.exp(10 * -0.044629)\n",
    "print(\" La température de mon thé au bout de 10 minutes sera de \",temperatureApres10,\" degrés\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant, on veut trouver la température du thé pour le temps t = 20.\n",
    "On réitère la même méthode. On voit qu'on trouve pareil que dans l'exo de mathématiques."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2072,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " La température de mon thé au bout de 20 minutes sera de  19.760059337998044  degrés\n"
     ]
    }
   ],
   "source": [
    "# Calcul avec python :\n",
    "import math \n",
    "temperatureApres20 = 30 - 25 * math.exp(20 * -0.044629)\n",
    "print(\" La température de mon thé au bout de 20 minutes sera de \",temperatureApres20,\" degrés\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Symbolique\n",
    "\n",
    "Maintenant qu'on a résolu au dessus avec une méthode numérique, on aimerait pouvoir résoudre avec SYMPY, symboliquement.\n",
    "\n",
    "## Etape 1 : Entrer l'eq diff dans SYMPY\n",
    "\n",
    "$$\n",
    "\\frac{dT}{dt}\n",
    "= K(T - 30)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2073,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = K \\left(y{\\left(t \\right)} - 30\\right)$"
      ],
      "text/plain": [
       "Eq(Derivative(y(t), t), K*(y(t) - 30))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "t   = sympy.Symbol('t')\n",
    "K   = sympy.Symbol('K') # On remarque qu'on a cette constante K inconnue pour l'instant\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(t),t)\n",
    "right = K * (y(t) - 30)\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Trouver la solution générale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2074,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = C_{1} e^{K t} + 30$"
      ],
      "text/plain": [
       "Eq(y(t), C1*exp(K*t) + 30)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(t)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : Préciser la condition initiale que T(0) = 5 degrés\n",
    "\n",
    "Au premier temps, la température du thé est de 5 degrés."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2075,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: -25}"
      ]
     },
     "execution_count": 2075,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t0 = 0\n",
    "y1 = 5\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(t,t0)) , dict=True)[0]\n",
    "consts\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 4 : Trouver l'équation de la température du thé en fonction du temps\n",
    "\n",
    "On voit qu'on trouve la même fonction solution que dans l'exercice de mathématiques\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2076,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(t \\right)} = 30 - 25 e^{K t}$"
      ],
      "text/plain": [
       "Eq(y(t), 30 - 25*exp(K*t))"
      ]
     },
     "execution_count": 2076,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 5 : Trouver la constante K\n",
    "\n",
    "On a toujours le même problème, on ne connait pas K, la question est de savoir si SYMPY peut résoudre ça automatiquement, et trouver la même solution que dans la résolution numérique.\n",
    "\n",
    "Alors, soit on le calcule à la main, soit SYMPY peut trouve ça automatiquement, je suis en train de regarder.\n",
    "\n",
    "En cours de résolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 6 : Quelle sera la température de mon thé après 5 minutes ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2077,
   "metadata": {},
   "outputs": [],
   "source": [
    "# En cours de résolution !\n",
    "# Pour l'instant, vu qu'on a pas trouvé K, \n",
    "# je ne sais pas le faire directement avec Sympy, faut le faire à la main avec le corollaire.\n",
    "# je recherche une lib permettant de résoudre l'eq à une inconnue K \n",
    "# # T5 = 30 - 25 ⅇ  ( 5 * K ) = 10 directement ( résolution en cours)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exemple 2 : Température d'un corps en fonction du temps ( Santé - Cadavre Enquête Police)\n",
    "--------------------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un cadavre est découvert à 15h45 dans une pièce où la température est de 20∘C. A cette époque, la température du corps est de 27∘C. Deux heures plus tard, à 17h45, la température du corps est de 25,3 ∘C. Quelle était l'heure du décès ? Notez que la température corporelle normale (humaine adulte) est de 37∘.\n",
    "\n",
    "Crédits : Joel Feldman, Andrew Rechnitzer, Elyse Yeager\n",
    "Liens : https://personal.math.ubc.ca/~CLP/CLP1/clp_1_dc/sec_newtonCooling.html\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/enquete.webp\">\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solution Nous supposerons que la température du corps obéit à la loi de refroidissement de Newton.\n",
    "\n",
    "Notons T(t) la température du corps à l'instant t, avec t=0 correspondant à 15h45. \n",
    "Nous souhaitons trouver l’heure du décès – appelez-la td.\n",
    "\n",
    "Il y a beaucoup de données dans l'énoncé du problème ; \n",
    "\n",
    "- on nous dit que la température ambiante : A=20\n",
    "- la température du corps lors de sa découverte : T(0)=27\n",
    "- la température du corps 2 heures plus tard : T(2)=25,3\n",
    "- en supposant que la personne était un adulte en bonne santé jusqu'à sa mort, la température au moment du décès : T(td)=37.\n",
    "\n",
    "\n",
    "## Solution numérique\n",
    "\n",
    "## Etape un : trouver l'équation de la température du corps en fonction du temps.\n",
    "\n",
    "On remplace les valeurs lues dans l'énoncé du problème du thé dans l'eq diff de NewTon, ça donne\n",
    "\n",
    "$$\n",
    "\\frac{dT}{dt}\n",
    "= K(T - 20)\n",
    "$$\n",
    "\n",
    "Puisque nous supposons que la température du corps obéit à la loi de refroidissement de Newton, nous utilisons le corollaire pour trouver l'équation T(t):\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/crol.png\">\n",
    "</div>\n",
    "\n",
    "On trouve T(t)\n",
    "\\begin{gather*}\n",
    "T(t) = [T(0)-A]\\,e^{Kt} + A\n",
    "=20+7 e^{Kt}\n",
    "\\end{gather*}\n",
    "\n",
    "Mais, Deux inconnues demeurent dans cette équation de la température du corps en fonction du temps, K et td.\n",
    "\n",
    "## Etape deux : trouver la constante K .\n",
    "Nous pouvons trouver la constante K en utilisant T(2)=25,3 :\n",
    "\n",
    "\\begin{align*}\n",
    "25.3=T(2)&= 20+7 e^{2K} & \\text{rearrange}\\\\\n",
    "7 e^{2K}&=5.3 & \\text{rearrange a bit more}\\\\\n",
    "2K &= \\log\\big(\\tfrac{5.3}{7}\\big)\\\\\n",
    "K &= \\tfrac{1}{2} \\log\\big(\\tfrac{5.3}{7}\\big) = -0.139 & \\text{to 3 decimal places}\n",
    "\\end{align*}\n",
    "\n",
    "## Etape trois : trouver Td (Time of death, heure du décès) .\n",
    "\n",
    "Puisque nous savons que td est déterminé par T(td)=37, nous avons\n",
    "\n",
    "\\begin{align*}\n",
    "37 = T(t_d) &= 20+7 e^{-0.139 t_d} & \\text{rearrange}\\\\\n",
    "e^{-0.139 t_d} &= \\tfrac{17}{7}\\\\\n",
    "-0.139 t_d &=\\log\\big(\\tfrac{17}{7}\\big)\\\\\n",
    "t_d &= -\\tfrac{1}{0.139}\\log\\big(\\tfrac{17}{7}\\big)\\\\\n",
    "& = - 6.38 &\\text{to 2 decimal places}\n",
    "\\end{align*}\n",
    "\n",
    "Maintenant, 6,38 heures équivaut à 6 heures et 0,38 × 60 = 23 minutes. L'heure du décès était donc 6 heures et 23 minutes avant 15h45, soit 9h22.\n",
    "\n",
    "## Solution Symbolique\n",
    "\n",
    "Maintenant qu'on a vu la méthode des profs de https://personal.math.ubc.ca/ pour obtenir la solution numériquement, on aimerait pouvoir le faire avec SYMPY, et que tout soit automatisé, voir pour le mettre dans un programme ensuite ... \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2078,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A venir"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <b>Cas pratique 6 : Evolution d'un capital dont le taux de croissance est proportionnel au capital présent</b>\n",
    "--------------------------------------------------------------------------------------------------\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/capital.jpg\">\n",
    "</div>\n",
    "\n",
    "Source : Promaths - https://www.youtube.com/watch?v=wCgaZc_dUhA&t=316s\n",
    "\n",
    "Un capital de 8000 frs est placé sur un compte dont le taux de croissance du capital au temps t \n",
    "est proportionnel au capital présent dans ce compte à ce moment.\n",
    "\n",
    "- 1.Déterminer l'expression du capital C(t) en fonction du temps si la constante de proportionnalité (k) corresponds\n",
    "à un intérêt de 3% par exemple.\n",
    "- 2.Déterminer le capital acquis au bout de 5 ans selon ce modèle.\n",
    "\n",
    "\n",
    "$$\n",
    "\\frac{dc}{dt}\n",
    "= k . C\n",
    "$$\n",
    "\n",
    "où\n",
    "- dc/dt est le capital en fonction du temps\n",
    "- k est le taux de croissance du capital\n",
    "- C est le capital "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution graphique"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2079,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Taux\n",
    "k = 0.03\n",
    "\n",
    "# Equation\n",
    "def deriv (y,x) :\n",
    "    return   y * k\n",
    "\n",
    "#  Time points\n",
    "x = np.linspace ( 0 , 10)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 8000\n",
    "\n",
    "# Résoudre l'équation diff\n",
    "solution = odeint ( deriv , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# Dessiner le résultat\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Capital\" )\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution symbolique\n",
    "## Etape 1 : Entrer l'équation différentielle dans SYMPY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2080,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 0.03 y{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 0.03*y(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x) # Partie gauche, avec la dérivée\n",
    "right = y(x) * k\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : Trouver la solution générale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2081,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{0.03 x}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(0.03*x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 3 : Entrer une condition initiale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2082,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: 8000}"
      ]
     },
     "execution_count": 2082,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 0\n",
    "u0 = 8000\n",
    "consts = sympy.solve( sympy.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 4 : Equation du capital en fonction du temps\n",
    "\n",
    "Grace aux 3 étapes précédentes, on sait que pour trouver mon capital en fonction du temps, \n",
    "l'équation est :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2083,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = 8000 e^{0.03 x}$"
      ],
      "text/plain": [
       "Eq(y(x), 8000*exp(0.03*x))"
      ]
     },
     "execution_count": 2083,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 5 : Trouver mon capital au bout de la cinquième année\n",
    "\n",
    "On voit qu'on trouve le même résultat que la chaine youtube ProMaths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2084,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Au bout de 5 ans, mon capital sera de :  9294.673941826264  euros\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "capital = 8000 * math.exp(0.03 * 5)\n",
    "print(\" Au bout de 5 ans, mon capital sera de : \",capital,\" euros\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cas pratique 7 : Force constante sur un objet\n",
    "-------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "Michel Van Biezen : https://www.youtube.com/watch?v=cioi4lRrAzw&list=PLX2gX-ftPVXV10J9jL1Lb46pPQVgBbL4Q&index=5\n",
    "\n",
    "On a un objet m, sur lequel on applique une force constante F, et d'accéleration a .\n",
    "F = ma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2085,
   "metadata": {},
   "outputs": [],
   "source": [
    "# A VENIR CREATION EN COURS !!!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color:green\">3. Résoudre une équation différentielle d'ordre 1 avec second membre <b>constant</b> -> y' = ax + b</span>\n",
    "\n",
    "--------------------------------------------------------------------------------------------------\n",
    "\n",
    "## Cas pratique\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/tarte-four.jpg\">\n",
    "</div>\n",
    "\n",
    "Source : https://www.youtube.com/watch?v=3X1m6triQzA\n",
    "\n",
    "Je viens de sortir ma tarte à la morue du four.\n",
    "Sa température est de 200 degrés.\n",
    "Je remarque que sa température est fonction du temps T(t) en heure et suit une équation différentielle:\n",
    "\n",
    "$$ y' + 1.4y = 30 $$\n",
    "\n",
    "a/ Donnez l'expression de g(t) en fonction de t , c'est à dire , résoudre l'équation différentielle\n",
    "\n",
    "b/ Quelle sera la température de ma tarte après 30 minutes ?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2086,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"800\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/3X1m6triQzA\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x2404634b910>"
      ]
     },
     "execution_count": 2086,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('3X1m6triQzA', width=800, height=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Mise au bon format de l'équation différentielle\n",
    "\n",
    "avant de pouvoir l'entrer dans Sympy, il faut d'abord la mettre au bon format :\n",
    "\n",
    "$$ y' = ay + b $$\n",
    "\n",
    "Donc :\n",
    "\n",
    "$$ y' + 1.4y = 30 $$\n",
    "\n",
    "Nous donne : \n",
    "\n",
    "$$ y' = -1.4y + 30 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 1 : Entrer l'équation différentielle dans sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2087,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 30 - 1.4 y{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 30 - 1.4*y(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "\n",
    "right = -1.4 * y(x) + 30\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 2 : Afficher la solution générale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2088,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{- 1.4 x} + 21.4285714285714$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(-1.4*x) + 21.4285714285714)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 3 : Déterminer l’unique solution de l’équation telle que T(0) = 200 avec Sympy\n",
    "\n",
    "Comme explique le prof dans la vidéo youtube, on doit utiliser cette technique pour ensuite obtenir une équation qui nous permette de savoir la température à tout temps donné. On sait qu'au temps 0, quand on la sort du four, elle est de 200 degrés.\n",
    "\n",
    "Il faut Entrer la condition, La condition est une constante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2089,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{C1: 178.571428571429}"
      ]
     },
     "execution_count": 2089,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x0 = 0\n",
    "y1 = 200\n",
    "consts = sympy.solve( sympy.Eq( y1, solgen.rhs.subs(x,x0)) , dict=True)[0]\n",
    "consts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 4 : Equation de la température de ma tarte en fonction du temps \n",
    "\n",
    "Grace aux 3 étapes précédentes, on sait que pour trouver la température de ma tarte en fonction du temps en heure, \n",
    "l'équation est ( On trouve le même résultat que le prof dans la vidéo ...) : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2090,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = 21.4285714285714 + 178.571428571429 e^{- 1.4 x}$"
      ],
      "text/plain": [
       "Eq(y(x), 21.4285714285714 + 178.571428571429*exp(-1.4*x))"
      ]
     },
     "execution_count": 2090,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solpar = solgen.subs(consts)\n",
    "solpar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Etape 5 : Quelle sera la température de ma tarte après 30 minutes ?\n",
    "\n",
    "On se sert de l'équation trouvée à l'étape 4, pour trouver la température !\n",
    "Vu que c'est en heure, 30 minutes = 0.5 heures !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2091,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " La température de ma tarte au bout de 30 minutes sera de  110.09623086863958  degrés\n"
     ]
    }
   ],
   "source": [
    "import math \n",
    "temperature = 21.42 + 178.572 * math.exp(-1.4 * 0.5)\n",
    "print(\" La température de ma tarte au bout de 30 minutes sera de \",temperature,\" degrés\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <b>Cas pratique 2 : Charge d'un condensateur.</b>\n",
    "------------------------------------------------------------------------------------------------------------------------\n",
    "\n",
    "<div style=\"text-align:center\">\n",
    "<img src=\"img/condensateur.jpg\">\n",
    "</div>\n",
    "\n",
    "On résume la charge d'un condensateur en fonction du temps par l'equation diff suivante :\n",
    "\n",
    "\n",
    "$$\n",
    "\\frac{du(t)}{dt} = \\frac{U - u(t)}{R\\,C}\n",
    "$$\n",
    "\n",
    "avec pour condition initiale\n",
    "\n",
    "$$\n",
    "u(t=0)=0\n",
    "$$\n",
    "\n",
    "car le condensateur est déchargé au temps 0\n",
    "\n",
    "Oû \n",
    "- du(t)/dt signifie \"l'évolution de la tension en fonction du temps\"\n",
    "- dt signifie \" en fonction du temps\"\n",
    "- u signifie la tension exprimée en volts\n",
    "- R est la resistance en Ohms\n",
    "- C est lié à l'intensité en Farads( Lire la doc)\n",
    "\n",
    "Source : \n",
    "https://cpge.frama.io/fiches-cpge/Python/%C3%89quation%20diff%C3%A9rentielle/0-Equation%20diff%C3%A9rentielle/#exemple-systeme-masseressort\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution graphique\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2092,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.integrate import solve_ivp\n",
    "import numpy as np\n",
    "\n",
    "# Constantes du système\n",
    "R = 10  # Ohms\n",
    "C = 0.01  # F\n",
    "U = 5  # V\n",
    "\n",
    "# Définition de l'équation différentielle\n",
    "def equation(t, u):\n",
    "    return (U-u)/(R*C) # On reconnait bien l'équation différentielle\n",
    "\n",
    "t0 = 0\n",
    "tf = 0.8  # seconde\n",
    "u0 = 0  # Condition initiale\n",
    "\n",
    "# Résolution\n",
    "tension = solve_ivp(equation, [t0, tf], [u0])\n",
    "\n",
    "# Calcul du courant traversant le condensateur\n",
    "courant = (U-tension.y[0])/R\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Tracé de la tension aux bornes du condensateur\n",
    "plt.plot(tension.t, tension.y[0], label=\"u(t)\")\n",
    "plt.plot(tension.t, courant, label=\"i(t)\")\n",
    "plt.ylabel('u(t) en V et i(t) en A')\n",
    "plt.xlabel(\"Temps (s)\")\n",
    "plt.title(\"Tension aux bornes du condensateur et courant le traversant\")\n",
    "plt.grid(which=\"both\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <span style=\"color:green\">4. Résoudre une équation différentielle d'ordre 1 avec second membre variable -> y' = ax + x²</span>\n",
    "-------------------------------------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2093,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/jpeg": 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",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"800\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/Xd9bKiQgzp8\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x2403d163340>"
      ]
     },
     "execution_count": 2093,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('Xd9bKiQgzp8', width=800, height=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Source : https://www.youtube.com/watch?v=Xd9bKiQgzp8\n",
    "\n",
    "## <strong><span style=\"color:red\"> y' - 2y = x²<span></strong>\n",
    "\n",
    "Contrairement à Yvan Monka qui résouds à la main, en trouvant d'abord la solution générale de l'équation homogène, puis une solution particulière à l'équation originelle; on entre directement l'équation dans SYMPY, qui résouds et trouve directement la même solution que Yvan Monka, ce qui prouve que le processus est bon .\n",
    "\n",
    "## Etape 1 :  On entre l'équation dans Sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2094,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = x^{2} + 2 y{\\left(x \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), x**2 + 2*y(x))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "left  = sympy.diff(y(x),x)\n",
    "\n",
    "right = x ** 2 + 2 * y(x) # La fonction y s'écrit y(x)\n",
    "\n",
    "edo = sympy.Eq( left , right )\n",
    "display(edo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Etape 2 : on affiche la solution\n",
    "\n",
    "La solution est identique que celle que Yvan Monka a trouvé avec le calcul à la main au tableau."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2095,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} e^{2 x} - \\frac{x^{2}}{2} - \\frac{x}{2} - \\frac{1}{4}$"
      ],
      "text/plain": [
       "Eq(y(x), C1*exp(2*x) - x**2/2 - x/2 - 1/4)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANNEXES\n",
    "\n",
    "# <b>Comparaison avec les suites géométrique</b>\n",
    "\n",
    "Imaginons un capital élevé au carré à chaque intervalle de temps , on pourrait se dire que \" chouette, notre équation différentielle du début va résoudre ce problème, et que ça va aller \"... Ben non, en fait.\n",
    "\n",
    "\n",
    "Calculons à la main :<br>\n",
    "temps 1 = 1² = 1<br>\n",
    "temps 2 = 2² = 4<br>\n",
    "temps 3 = 4² = 16<br>\n",
    "temps 4 = 16² = 256<br>\n",
    "temps 5 = 256² = 65536<br>\n",
    "etc ...\n",
    "\n",
    "Chaque jour, le capital est élevé au carré.\n",
    "Ce capital suit une progression géométrique de raison au carré.\n",
    "\n",
    "On voit que la suite géométrique <b>n'a pas de rapport avec la fonction f(x) = x² ni avec notre équation différentielle initiale</b>, car si on imagine trouver le capital au temps 10 avec cette fonction f(x) = x² , on fait f(10) = 10², ce qui \n",
    "nous donne un résultat de 100, qui est faux si l'on veut un capital multiplié au carré à chaque intervalle de temps de façon cumulative.\n",
    "L'équation différentielle présentée au dessus ne convient donc pas, donc prudence ."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Suite géométrique incrémentée par pourcentage\n",
    "\n",
    "Imaginons maintenant un capital multiplié par 2 % à chaque intervalle de temps .\n",
    "Le capital commence à 1. Là, on se dit que ça ressemble bien à notre equation diff du début, que ca va marcher... Pas de chance, non, ce n'est pas pareil.\n",
    "\n",
    "On calcule la suite géométrique:\n",
    "\n",
    "temps 1 = 1 + (1 * 2/100) = 1.02 <br>\n",
    "temps 2 = 1.02 + (1.02 * 2/100) = 1.02 + 0.0204 = 1.0404 <br>\n",
    "temps 3 = 1.0404 + (1.0404 * 2/100)  = 1.0404 + 0.020808 = 1.061208<br>\n",
    "\n",
    "etc ...\n",
    "On trouve directement le capital au jour 3 avec la formule : \n",
    "u(n) = 100 * 1.02 ** 3\n",
    "\n",
    "Source : https://www.maths-et-tiques.fr/telech/SuitesTESL1.pdf\n",
    "\n",
    "On appelle ça une suite géométrique de raison 1.02 qui équivaut à 2%\n",
    "\n",
    "<b>Là encore, aucun rapport avec le résultat de notre équation différentielle du début et on va le prouver ensuite</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2096,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0612080000000002"
      ]
     },
     "execution_count": 2096,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Notre capital au temps 3\n",
    "un = 1 * 1.02 ** 3\n",
    "un"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dessiner la suite géométrique incrémentée en %\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2097,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Au temps 3, la valeur de mon capital sera de  1.061208\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def u(n):\n",
    "    if n == 0:\n",
    "        return 1 # valeur de u(0)\n",
    "    \n",
    "    return u(n-1) * 1.02 \n",
    "\n",
    "x = [ n for n in range(10) ] \n",
    "y = [ u(n) for n in range(10) ]\n",
    "\n",
    "\n",
    "plt.scatter(x , y , c = 'coral' , label = 'u(n): q > 1')\n",
    "\n",
    "\n",
    "plt.title('Suite géométrique de raison 1.02 ( 0.2%)')\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.legend()\n",
    "\n",
    "plt.show()\n",
    "print(\" Au temps 3, la valeur de mon capital sera de \" ,np.interp(3, x, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# L'équation diff ne donne pas le même résultat\n",
    "\n",
    "On voit sur des forums que l'équation différentielle y' = 0.02x serait pratique lors du calcul de croissance de capital d' un taux de 2%, et on sous entends, que le résultat serait le même qu'une suite géométrique, c'est ce qu'on va voir en dessous.\n",
    "\n",
    "On voit que le résultat n'est absolument pas le même, ce qui est logique puisque les calculs ne sont pas les mêmes.\n",
    "\n",
    "\n",
    "$$ y' = 0.02x $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2098,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Au temps 3, ma valeur sera de  1.0900249895907752\n"
     ]
    }
   ],
   "source": [
    "# Notre taux de 2 %\n",
    "taux = 0.02\n",
    "\n",
    "# fonction qui retourne la dérivée pour chaque x fourni à la fonction np.linspace\n",
    "def derivee (y,x) :\n",
    "    return taux * x\n",
    "\n",
    "#  time points\n",
    "x = np.linspace ( 0 , 5)\n",
    "\n",
    "# Condition initiale\n",
    "y0 = 1\n",
    "\n",
    "# solve ODE\n",
    "solution = odeint ( derivee , y0 , x )\n",
    "y = solution [ : , 0 ]\n",
    "\n",
    "# plot results\n",
    "plt.plot ( x , y )\n",
    "plt.title(\"Equation diff y' = 0.02x  \" )\n",
    "plt.ylabel(\"valeur\")\n",
    "plt.xlabel(\"temps\")\n",
    "plt.show()\n",
    "\n",
    "# Trouver la valeur au temps 3 avec l'interpolation graphique\n",
    "# On voit que ce n'est pas le résultat précis\n",
    "print(\" Au temps 3, ma valeur sera de \" ,np.interp(3, x, y))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2099,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d}{d x} y{\\left(x \\right)} = 0.02 x$"
      ],
      "text/plain": [
       "Eq(Derivative(y(x), x), 0.02*x)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y{\\left(x \\right)} = C_{1} + 0.01 x^{2}$"
      ],
      "text/plain": [
       "Eq(y(x), C1 + 0.01*x**2)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Ma valeur au bout de 3 temps est de  1.09\n"
     ]
    }
   ],
   "source": [
    "from sympy import Function, dsolve, Eq, Derivative, sin, cos, symbols\n",
    "from sympy.abc import x\n",
    "import sympy\n",
    "\n",
    "x   = sympy.Symbol('x')\n",
    "y   = sympy.Function('y')\n",
    "\n",
    "# On crée notre eq diff\n",
    "partie_gauche  = sympy.diff(y(x),x)\n",
    "partie_droite = 0.02 * x\n",
    "\n",
    "# Afficher l'eq diff\n",
    "edo = sympy.Eq( partie_gauche , partie_droite )\n",
    "display(edo)\n",
    "\n",
    "# Afficher la solution générale\n",
    "solgen = sympy.dsolve(edo,y(x)) \n",
    "display(solgen)\n",
    "\n",
    "# Afficher une solution particullière en utilisant l'eq de la solution générale\n",
    "# Notre valeur au temps 3\n",
    "valeur = 1 + 0.01 * 3 ** 2\n",
    "print (\" Ma valeur au bout de 3 temps est de \" , valeur)"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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   "file_extension": ".py",
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