8.8

from scipy.integrate import odeint
import numpy as np
import pylab as plt

yx = lambda y,x: [y[1], np.sqrt(1+y[1]**2)/5/(1-x)]
x0 = np.arange(0, 1, 0.00001)
y0 = odeint(yx, [0,0], x0)
plt.rc('font', size=16)
plt.plot(x0, y0[:,0]); plt.show()