Euler method Generalisation

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint

%matplotlib inline


def F(t,k):
    x,y,z = k

    Q = np.empty(3)
    Q[0] = x  + 3

    Q[1] = x  + 3 *y +z

    Q[2] = x  + y**2

    return Q

def EulerMethod(a,b,c,N,F):
    H = (b-a)/N

    t = np.linspace(a,b,N+1)

    Z = np.zeros((N+1,len(c)))

    Z[0,:] = c
    for k in range(0,N):
        Z[k+1] = Z[k] +  H*F(t[k],Z[k])
    return t,Z



a = 0
b = 1
N = 100
c = np.array([1,2,1])


t,result = EulerMethod(a,b,c,N,F)
result