-1

Could someone please help me im trying to

Use the fourth order Runge-Kutta algorithm to solve the differential equation.

dy/dx = -y, y(0) = 1

nelow is the program I currently have, and do not know how to corect it, I shouls get altering values of y as x goes from 0 to 5 at increments of 0.1, and then when plotted in a graph should produce a curve... Currently my program does the x bit right but falls apart with y in that i have problably missed a step required to get sensible values.... im very new to this programming so it may even be a obvious mistake..... any help would be awesome

```
/* A Runge-Kutta Method for solving Differential Equations*/
/* dy/dt = -y(t), y(0)=1, 0<=x<=5, start h=0.1*/
#include <stdio.h>
#define dist 0.1 /* stepsize */
#define xf 5 /* max for x */
FILE *output; /* internal filename */
double rkutta( double x, double y, double h); /*Runge Kutta Function */
double F(double x, double y); /*Function derivative*/
main()
{
double x, y, h;
int n;
output=fopen("xydata.dat", "w"); /* External filename */
h=0.1;
y=1; /* Initial condition */
fprintf(output, "0\t%f\n", y);
for (n=0;dist*n<=xf;n++) /* The time loop */
{
x=n*dist;
y-=rkutta(x, y, dist);
fprintf (output, "%f\t%f\n", x, y);
}
fclose(output);
} /* End of main function*/
double rkutta(double x, double y, double h) /*Called on RK function*/
{
double yn, k1, k2, k3, k4;
double H = h/2.0;
k1 = (h*F(x, y));
k2 = (h*F(x+H, y+(k1/2)));
k3 = (h*F(x+H, y+(k2/2)));
k4 = (h*F(x+h, y+k3));
return(y+=(y+(k1+2*k2+2*k3+k4)*1/6));
}
double F(double x, double y) /*Called on derivative*/
{
return (y);
}
```