import numpy as np

x0 = 1.7
xk = 2.7
h = 0.1
y0 = 5.3

def f(x, y):
    return x**2 + np.cos(y / np.pi)

def runge_kutta_4(f, x0, y0, h, xk):
    n = int((xk - x0) / h) + 1
    x = [x0 + i * h for i in range(n)]
    y = [0] * n
    y[0] = y0

    print("Tabela wyników:")
    print(f"{'i':<5}{'x':<10}{'y':<15}{'k1':<10}{'k2':<10}{'k3':<10}{'k4':<10}{'Δy':<10}")

    for i in range(1, n):
        k1 = h * f(x[i-1], y[i-1])
        k2 = h * f(x[i-1] + h/2, y[i-1] + k1/2)
        k3 = h * f(x[i-1] + h/2, y[i-1] + k2/2)
        k4 = h * f(x[i-1] + h, y[i-1] + k3)
        Δy = (k1 + 2*k2 + 2*k3 + k4) / 6
        y[i] = y[i-1] + Δy
        print(f"{i-1:<5}{x[i-1]:<10.2f}{y[i-1]:<15.5f}{k1:<10.5f}{k2:<10.5f}{k3:<10.5f}{k4:<10.5f}{Δy:<10.5f}")

    print(f"{n-1:<5}{x[-1]:<10.2f}{y[-1]:<15.5f}")

    return x, y

x, y = runge_kutta_4(f, x0, y0, h, xk)