#include<stdio.h>
#include <math.h>
#include<conio.h>
//dy/dx = 1 + y^2#define F(x,y)  1 + (y)*(y)
void main()
{
    double y0,x0,y1,n,h,f,k1,k2,k3,k4;
    clrscr();
    printf("\nEnter the value of x0: ");
    scanf("%lf",&x0);
    printf("\nEnter the value of y0: ");
    scanf("%lf",&y0);
    printf("\nEnter the value of h: ");
    scanf("%lf",&h);
    printf("\nEnter the value of last point: ");
    scanf("%lf",&n);
    for(; x0<n; x0=x0+h)
    {
        f=F(x0,y0);
        k1 = h * f;
        f = F(x0+h/2,y0+k1/2);
        k2 = h * f;
        f = F(x0+h/2,y0+k2/2);
        k3 = h * f;
        f = F(x0+h/2,y0+k2/2);
        k4 = h * f;
        y1 = y0 + ( k1 + 2*k2 + 2*k3 + k4)/6;
        printf("\n\n  k1 = %.4lf  ",k1);
        printf("\n\n  k2 = %.4lf ",k2);
        printf("\n\n  k3 = %.4lf ",k3);
        printf("\n\n  k4 = %.4lf ",k4);
        printf("\n\n  y(%.4lf) = %.3lf ",x0+h,y1);
        y0=y1;
    }
    getch();
}

/*
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         OUT PUT
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Enter the value of x0: 0

Enter the value of y0: 0

Enter the value of h: 0.2

Enter the value of last point: 0.4


     k1 = 0.2000

     k2 = 0.2020

     k3 = 0.2020

     k4 = 0.2020

       y(0.2000) = 0.202

     k1 = 0.2081

     k2 = 0.2187

     k3 = 0.2193

     k4 = 0.2193

       y(0.4000) = 0.419


*/