import math
import matplotlib.pyplot as plt
import numpy as np

u1 = []
u2 = []
x = []
i = 0
a = 0.0
b = 1.0
h = 0.05
n = (b-a)/h
k = 0.0

u1.append(0.0)
u2.append(1.0)
x.append(0.0)

while i < n:
    u1.append(u1[i]+h*u2[i])
    u2.append(u2[i]+h*(-2*(math.tan(k))*u2[i]-(1.0-math.tan(k))*u1[i]+(1.0-math.tan(k))*(math.asin(math.tan(k)))))
    i+=1
    k+=h
    x.append(k)

print(u1,x)