Method to find solution of ordinary differential equations

ODE-Midpoint.py

#Midpoint Method for solutions approach
import math, sys 
import numpy as np

def Midpoint(f, y0, T, n):
    """Solve y'=f(t,y), y(0)=y0, with n steps until t=T."""
    dt = T/float(n)
    t = np.zeros(n+1)
    y = np.zeros(n+1)  # y[k] is the solution at time t[k]
    y[0] = y0
    t[0] = 0
    for k in range(n):
        t[k+1] = t[k] + dt
        y[k+1] = y[k] + dt*f(y[k], t[k]+(dt/2) +(dt/2)*f(y[k],t[k]))
    return y, t

# Problem: y'=y
def f(t, y): 
    return y