from numpy import *;
import matplotlib.pyplot as plt;

f = lambda x,t: x
exact = lambda t: exp(t);

n = 2;
a = 0;
b = 1
x0 = 1;


x = zeros(n+1);
t = linspace(a, b, n+1);
x[0] = x0; 
h = float(b-a)/n;

for k in range(n):
    x[k+1] = x[k] + h*f(x[k], t[k])


plt.plot(t,x);
y = linspace(a,b,101);
plt.hold('on');
plt.plot(y, exact(y));
plt.legend(['Euler', 'Exact']);
plt.xlabel('t');
plt.ylabel('x(t)');
plt.show();