#!/usr/bin/python3
# Euler's method (explicit variant)

import numpy as np
import matplotlib.pyplot as plt

def f(x, t):
    return -x**3 + np.sin(t)
    
a, b, = 0.0, 10.0        # interval
N = 1000                 # number of points
h = (b - a) / N          # increment
x = 0.0                  # initial condition

tpoints = np.linspace(a, b, N+1)
xpoints = []

for t in tpoints:
    xpoints.append(x)
    x += h * f(x, t)
    
plt.xlabel("t")
plt.ylabel("x(t)")    
plt.plot(tpoints, xpoints)
plt.show()