Question

Write a C program to solve the following differential equation using
Runge-Kutta method. Step size h=0.3
10 dy/dx+ 3y^3 = x(x + 1),y(0.3) = 5
Find y(x) for different values of x ​

Answer 1

#include<stdio.h>

#include<math.h>

float f(float x,float y);

int main()

{

float x0,y0,m1,m2,m3,m4,m,y,x,h,xn;

printf("Enter x0,y0,xn,h:");

scanf("%f %f %f %f",&x0,&y0,&xn,&h);

x=x0;

y=y0;

printf("\n\nX\t\tY\n");

while(x<xn)

{

m1=f(x0,y0);

m2=f((x0+h/2.0),(y0+m1*h/2.0));

m3=f((x0+h/2.0),(y0+m2*h/2.0));

m4=f((x0+h),(y0+m3*h));

m=((m1+2*m2+2*m3+m4)/6);

y=y+m*h;

x=x+h;

printf("%f\t%f\n",x,y);

}

}

float f(float x,float y)

{

float m;

m=(x-y)/(x+y);

return m;

}

Answer 2

Explanation:

Test Case 1 -

0.9

y=1.7772

Test Case 2

1.2

y=1.4681