#include <iostream>
#include <math.h>
#include <iomanip>

using namespace std;

/*
double f(double x,double y,double z){
    return (z*y+x);
}

double g(double x,double y,double z){
    return (z*x+y);
}




void rungeKuta2equacoes(double x0,double y0,double z0, double h,double lim,double &yn,double &zn){
    double xn=x0;
    yn=y0;
    zn=z0;
    int n=(lim-x0)/h;


    do{
        x0=xn;
        y0=yn;
        z0=zn;
        double d1= h*f(x0,y0,z0);
        double k1= h*g(x0,y0,z0);
        double d2= h*f(x0 + (h/2),yn + d1/2,z0 + (k1/2));
        double k2= h*g(x0+(h/2),y0+(d1/2),zn + (k1/2));
        double d3= h*f(x0+(h/2),yn+(d2/2),zn + (k2/2));
        double k3= h*g(x0+(h/2),y0+(d2/2),z0+(k2/2));
        double d4= h*f(x0+h,yn+d3,z0+k3);
        double k4= h*g(x0+h,y0+d3,z0+k3);
        xn = x0+h;
        yn = y0+(d1/6)+(d2/3)+(d3/3)+(d4/6);
        zn = z0+(k1/6)+(k2/3)+(k3/3)+(k4/6);
        n--;
    }while(n>=0);

    cout << "Syn-> " << yn << endl;
    cout << "Szn-> " << zn << endl;
}


/*
int main(){
    double syn;
    double s1yn;
    double s2yn;
    double szn;
    double s1zn;
    double s2zn;


    cout << "S" << endl;
    rungeKuta2equacoes(0,1,1,0.1,0.5,syn,szn);
    cout << endl << "S`:" << endl;
    rungeKuta2equacoes(0,1,1,(0.1/2),0.5,s1yn,s1zn);
    cout << endl << "S``:" << endl;
    rungeKuta2equacoes(0,1,1,(0.1/4),0.5,s2yn,s2zn);

    cout << endl << "Qcyn-> " << (s1yn-syn)/(s2yn-s1yn) << endl;
    cout << "Qczn-> " << (s1zn-szn)/(s2zn-s1zn) << endl;
    cout << "Eyn-> " << (s2yn-syn)/15 << endl;
    cout << "Ezn-> " << (s2zn-szn)/15 << endl;

    return 0;
}
/**/