dydx

from numpy import *
import scipy as sp
import matplotlib.pyplot as plt
from scipy._lib.six import xrange


def f(x, y):
  return y


y0 = f(1, 1)
xmin = 0.
xmax = 10.
npoints = 150

dx = (xmax - xmin) / float(npoints)

x = sp.linspace(xmin, xmax, npoints)
forwardSol = x * 0.
forwardSol[0] = y0

for i in xrange(1, npoints):
  forwardSol[i] = forwardSol[i-1] + dx * f(forwardSol[i-1], forwardSol[i-1])

sol_exact = exp(x)

plt.figure()
plt.plot(x, forwardSol, '--r')
plt.plot(x, sol_exact, 'g')

plt.ylabel("forward")
plt.show()