#Second order diff. equation : d2y/dx2 = -y ; dp/dx = -y ; p = dy/dt
from pylab import *
from scipy import integrate
def derivative(X, t0): # X[0] is x, X[1] is dx/dt;
return [X[1], -X[0] ] # derivative of X[0] is X[1] , of X[1] is -y
start = [0,1] # x and dx/dt at t= 0
t = np.arange(0, 30, 0.01) # start time, stop and stepsize
result = integrate.odeint(derivative, start, t) # integrate
plot(t, result[:, 0]) # extract first column from 2d array
plot(t, result[:, 1]) # extract second column
show()