import matplotlib.pyplot as plt
from numpy import *

def f(t,x):
    return t + x

def x_exact(t):
    return -1-t + exp(t)


a = 0
b = 3

# Number of steps
N = 60
# Step length 
h = (b - a)/float(N)

x = zeros(N+1)
t = zeros(N+1)
x[0] = 0 # Initial condition
t[0] = a
for k in range(N):
    x[k+1] = x[k] + h*f(t[k], x[k])
    t[k+1] = t[k] + h

t_fine = linspace(a,b, 101)

plt.figure()
plt.plot(t, x, label='Euler')
plt.plot(t_fine, x_exact(t_fine), label='x(t)')
plt.xlabel('t')
plt.legend()
plt.show()