Method to find solution of ordinary differential equations

ODE-Taylor.py

#Taylor's Approach
import math, sys 
import numpy as np

def Taylor(f, y0, T, n):
    """Solve y'=f(t,y), y(0)=y0, with n steps until t=T."""
    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 #t0
    dt = T/float(n)
    print('h',dt)
    
    for k in range(n):
        t[k+1] = t[k] + dt  
        fk = f(y[k],t[k]) # f em t(k), y(k)
        dfk = dy(y[k],t[k]) # dy de f em t(k), y(k)
        ddfk = dyy(y[k],t[k]) # dyy de f em t(k), y(k)
        t1 = dt * fk
        t2 = ((dt**2)/2) * dfk * fk
        t3 = ((dt**3)/6) * ((ddfk * (fk**2)) + ((dfk**2) * fk))
        y[k+1] = y[k] + t1 + t2 + t3    
    return y, t

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