/*#include "pch.h"
#include <iostream>
using namespace std;
double fpochodna(double x, double y)
{

}
int main()
{
    system("PAUSE");
}*/
#include "pch.h"
#include <iostream>
using namespace std;

double f(double, double);
double fi_rk2(double, double, double);
double fi_rk4(double, double, double);

int main()
{
    double a, b, h;
    const int N = 10;
    cin >> a >> b;
    h = (b - a) / static_cast<double>(N);

    double y = 0.1, x = a;
    cout << "\nMetoda Eulera:\nx = " << x << " y = " << y << endl;
    for (int i = 0; i < N; i++) {
        y += h*f(x, y);
        x += h;
        cout << "x = " << x << " y = " << y << endl;
    }
    double(*fi)(double, double, double) = fi_rk2;
    y = 1.0, x = a;
    cout << "\nMetoda Rungego-Kutty (RK2):\nx = " << x << " y = " << y << endl;
    for (int i = 0; i < N; ++i) {
        y += h * fi(x, y, h);
        x += h;
        cout << "x = " << x << " y = " << y << endl;
    }

    y = 1.0, x = a;
    fi = fi_rk4;
    cout << "\nMetoda Rungego-Kutty (RK4):\nx = " << x << " y = " << y << endl;
    for (int i = 0; i < N; ++i) {
        y += h * fi(x, y, h);
        x += h;
        cout << "x = " << x << " y = " << y << endl;
    }
    system("pause");
    return 0;
}

inline double f(double x, double y) {
    return (y - x * x);
}

double fi_rk2(double x, double y, double h) {
    double k[2];
    k[0] = f(x, y),
        k[1] = f(x + h, y + h * k[0]);
    return 0.5*(k[0] + k[1]);
}

double fi_rk4(double x, double y, double h) {
    double k[4];
    k[0] = f(x, y),
        k[1] = f(x + 0.5*h, y + 0.5*h*k[0]),
        k[2] = f(x + 0.5*h, y + 0.5*h*k[1]),
        k[3] = f(x + h, y + h * k[2]);
    return (k[0] + 2.0*k[1] + 2.0*k[2] + k[3]) / 6.0;
}