TAY

import matplotlib
import matplotlib.pyplot as plt
import math

e = math.exp(1)
k = 8000
h =  0.00001

y0 = 0
z0 = 0
w0 = 16


w = [w0]
z = [z0]
y = [y0]
Y = [y0]
n = 1000000

x = [0]
for i in range(1, n):
    x.append(i*h)
    t = x[-1]
    Y.append(e**(-5*t) -e**(-t) + 4*t*e**(-t))

Delta = -1

for i in range(1,n):
    y.append(y[-1] + h*z[-1])
    z.append(z[-1] + h*w[-1])
    w.append(w[-1] + h*(-7*w[-1] - 11*z[-1] - 5 *y[-1]))
    if (i > k):
        Delta = max(Delta, abs(Y[i] - y[i])/Y[i])


print(Delta * 100)



plt.plot(x,y)
plt.plot(x,Y)