"""
=========================
Integrating a simple ODE
=========================

Solve the ODE dy/dt = -2y between t = 0..4, with the initial condition
y(t=0) = 1.
"""

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt

def f(t, y):
    return -2*y

t_span = (0, 4)  # time interval
t_eval = np.linspace(*t_span)  # times at which to evaluate `y`
y0 = [1, ]  # initial state
res = sp.integrate.solve_ivp(f, t_span=t_span, y0=y0, t_eval=t_eval)

plt.figure(figsize=(4, 3))
plt.plot(res.t, res.y[0])
plt.xlabel('t')
plt.ylabel('y')
plt.title('Solution of Initial Value Problem')
plt.tight_layout()
plt.show()