#include <stdio.h>
#include <math.h>

static double h=1.0/1024;
double exacty(double x){
    return x*x*cos(x);
}
double f(double x,double y){
    return 2/x*y-x*x*sin(x);
}
double fx(double x,double y){
    return -2*y/(x*x)-2*x*sin(x)-x*x*cos(x);
}
double fy(double x,double y){
    return 2/x;
}
double tstep(double x,double y){
    double t=f(x,y);
    return
    y+h*(t+h/2*(fx(x,y)+fy(x,y)*t));
}
int main(){
    double x,y;
    y=cos(1);
    int j;
    for(j=0;j<1024;j++){
        x=1+j*h;
        y=tstep(x,y);
    }
    x=1+j*h;
    double ye=exacty(x);
    printf("x=%22.14e\n",x);
    printf("yapprox=%22.14e\n",y);
    printf("yexact=%22.14e\n",ye);
    printf("yerror=%22.14e\n",fabs(y-ye));
    return 0;
}