Question

Consider the following differential equation: dydx=x+y

With initial condition: y = 1 when x = 0

1. Using the Euler forward method, solve this differential equation for the range x = 0 to x = 0.5 in increments (step) of 0.1
2. Check that the theoretical solution is y(x) = - x -1 , Find the error between the theoretical solution and the solution given by Euler method at x = 0.1 and x = 0.5 , correct to three decimal places

Answer 1

a)

code:

#include<stdio.h>
float fun(float x,float y)
{
float f;
f=x+y;
return f;
}
main()
{
float a,b,x,y,h,t,k;
printf("\nEnter x0,y0,h,xn: ");
scanf("%f%f%f%f",&a,&b,&h,&t);
x=a;
y=b;
printf("\n x\t y\n");
while(x<t)
{
k=h*fun(x,y);
y=y+k;
x=x+h;
printf("%0.3f\t%0.3f\n",x,y);
}
}

result:

b)