{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = symbols('f', cls=Function)\n",
    "R, freq, t,L,C = symbols('R f t L C')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(t \\right)}$"
      ],
      "text/plain": [
       "f(t)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d t^{2}} f{\\left(t \\right)} + \\frac{f{\\left(t \\right)}}{C L} = 0$"
      ],
      "text/plain": [
       "Eq(Derivative(f(t), (t, 2)) + f(t)/(C*L), 0)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffeq = Eq(f(t).diff(t,t)+f(t)/(L*C),0)\n",
    "diffeq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(t \\right)} = C_{1} e^{- t \\sqrt{- \\frac{1}{C L}}} + C_{2} e^{t \\sqrt{- \\frac{1}{C L}}}$"
      ],
      "text/plain": [
       "Eq(f(t), C1*exp(-t*sqrt(-1/(C*L))) + C2*exp(t*sqrt(-1/(C*L))))"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(diffeq, f(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{d^{2}}{d t^{2}} f{\\left(t \\right)} + \\frac{f{\\left(t \\right)}}{C L} = \\sin{\\left(2 \\pi f t \\right)}$"
      ],
      "text/plain": [
       "Eq(Derivative(f(t), (t, 2)) + f(t)/(C*L), sin(2*pi*f*t))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffeq2 = Eq(f(t).diff(t,t)+f(t)/(L*C), sin(2*pi*freq*t))\n",
    "diffeq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(t \\right)} = - \\frac{C L \\sin{\\left(2 \\pi f t \\right)}}{4 \\pi^{2} C L f^{2} - 1} + C_{1} e^{- t \\sqrt{- \\frac{1}{C L}}} + C_{2} e^{t \\sqrt{- \\frac{1}{C L}}}$"
      ],
      "text/plain": [
       "Eq(f(t), -C*L*sin(2*pi*f*t)/(4*pi**2*C*L*f**2 - 1) + C1*exp(-t*sqrt(-1/(C*L))) + C2*exp(t*sqrt(-1/(C*L))))"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(diffeq2, f(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle L \\frac{d^{2}}{d t^{2}} f{\\left(t \\right)} + R \\frac{d}{d t} f{\\left(t \\right)} + \\frac{f{\\left(t \\right)}}{C} = 0$"
      ],
      "text/plain": [
       "Eq(L*Derivative(f(t), (t, 2)) + R*Derivative(f(t), t) + f(t)/C, 0)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diffeq3 = Eq(L*f(t).diff(t,t)+R*f(t).diff(t)+f(t)/C, 0)\n",
    "diffeq3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f{\\left(t \\right)} = C_{1} e^{\\frac{t \\left(- R - \\frac{\\sqrt{C \\left(C R^{2} - 4 L\\right)}}{C}\\right)}{2 L}} + C_{2} e^{\\frac{t \\left(- R + \\frac{\\sqrt{C \\left(C R^{2} - 4 L\\right)}}{C}\\right)}{2 L}}$"
      ],
      "text/plain": [
       "Eq(f(t), C1*exp(t*(-R - sqrt(C*(C*R**2 - 4*L))/C)/(2*L)) + C2*exp(t*(-R + sqrt(C*(C*R**2 - 4*L))/C)/(2*L)))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dsolve(diffeq3, f(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6"
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 },
 "nbformat": 4,
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