import matplotlib.pyplot as plt
import math


def f(x):
    return 1 / math.sqrt(2) * (x - 1) / math.sqrt(x - math.log(x))


def df(x, y):
    return y / (x - 1) - y ** 3 / (x * x - x)


a = 0.03
b = 0.97

eps = 1.0
n = 1

while eps > 0.0001:

    x0 = a
    y0 = f(x0)

    x = []
    y = []
    y2 = []
    h = (b - a) / n

    x.append(x0)
    y.append(y0)
    y2.append(y0)

    for i in range(1, n + 1, 1):
        k1 = h * df(x[-1], y[-1])
        k2 = h * df(x[-1] + h / 2, y[-1] + k1 / 2)
        k3 = h * df(x[-1] + h / 2, y[-1] + k2 / 2)
        k4 = h * df(x[-1] + h, y[-1] + k3)

        y.append(y[-1] + 1 / 6 * (k1 + 2 * k2 + 2 * k3 + k4))
        x.append(x0 + i * h)
        y2.append(f(x[-1]))

    eps = math.fabs(f(b) - y[-1])

    print(f"n = {n},\nh = {h},\neps = {eps},\ny(b) = {y[-1]}")
    plt.plot(x, y, color='red')
    plt.plot(x, y2, color='green')
    plt.show()
    n *= 2