#include<stdio.h>
#include <math.h>
#include<conio.h>
#define F(x,y)  1 + (y)*(y)
void main()
{
  double y0,x0,y1,y[10],n,h,f,sum=0;
  int j;
  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 X for finding Y(x): ");
  scanf("%lf",&n);
  for(x0,j=0; x0<n; x0=x0+h,j++)
  {
    printf("\nEnter the value of Y(%.2lf): ",x0);
    scanf("%lf",&y[j]);
  }

    f = F(x0,y[1]);
    sum = sum + 2 * f;
    f = F(x0,y[2]);
    sum = sum - f;
    f = F(x0,y[3]);
    sum = sum + 2 * f;
    y1 = y[0] + (4*h/3) * (sum);
    printf("\n\n  Yp(%.2lf) = %.3lf ",n,y1);

    sum = 0;
    f=F(x0,y[2]);
    sum = sum + f;
    f = F(x0,y[3]);
    sum = sum + 4 * f;
    f = F(x0,y1);
    sum = sum + f;
    y1 = y[2] + (h/3) * (sum);
    printf("\n\n  Yc(%.2lf) = %.3lf ",n,y1);

getch();
}

/*
____________________________________

         OUT PUT
____________________________________


Enter the value of x0: 0

Enter the value of y0: 0

Enter the value of h: 0.2

Enter the value of X for finding Y(x): 0.8

Enter the value of Y(0.00): 0

Enter the value of Y(0.20): 0.2027

Enter the value of Y(0.40): 0.4228

Enter the value of Y(0.60): 0.6841


  Yp(0.80) = 1.024

  Yc(0.80) = 1.029


*/