import matplotlib.pyplot as plt
import numpy as np
from scipy.integrate import solve_ivp


def f(t, y):
    """this is the rhs of the ODE to integrate, i.e. dy/dt=f(y,t)"""
    return -2 * y


y0 = [10]  # initial value y0=y(t0)
t0 = 0  # integration limits for t: start at t=0
tf = 2  # and finish at t=2
t_eval = np.linspace(t0, tf, 50)

sol = solve_ivp(fun=f, t_span=[t0, tf], y0=y0, t_eval=t_eval)

fig, ax = plt.subplots()
ax.plot(sol.t, sol.y[0], "o-")
ax.set_xlabel("t")
ax.set_ylabel("y(t)")
fig.savefig("odeintexample1.pdf")