#!/usr/bin/env python
# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt

plt.axes().set_aspect('equal')
plt.xlabel("X values")
plt.ylabel("Y values")
plt.title("Differential Equation Example")
plt.grid()

# critical time step value
Δt = 0.25

ox = x = 0
y = 1
total = 0

xvals = []
yvals = []

while ox <= 0 or x > 0:
  ox = x
  x -= y * Δt
  y += x * Δt
  total += Δt
  xvals += [x]
  yvals += [y]
  
print(f"𝜏 = {total:.7f}")

print(f"𝜋 = {total/2:.7f}")

plt.plot(xvals,yvals)
plt.savefig("diffeq_example1.png")