Method to find solution of ordinary differential equations

ODE-RungeKutta4.py

#Runge Kutta 4th
import math, sys 
import numpy as np

def RungeKutta4(f, y0, T, n):
    t = np.zeros(n+1)
    y = np.zeros(n+1)
    y[0] = y0
    t[0] = 0
    dt = T/float(n)
    for k in range(n):
        t[k+1] = t[k] + dt
        K1 = dt * f(y[k], t[k])
        K2 = dt * f(y[k] + 0.5*K1, t[k] + 0.5*dt)
        K3 = dt * f(y[k] + 0.5*K2, t[k] + 0.5*dt)
        K4 = dt * f(y[k] + K3, t[k] + dt)
        y[k+1] = y[k] + (1/6.0)*(K1 + 2*K2 + 2*K3 + K4)
    return y, t

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