//include math.h to get the sqrt command
#include <math.h>

...

//ax and ay should be stored from the previous loop.
vx+=ax*dt/2.0;
vy+=ay*dt/2.0;

//Calculate the vector acceleration. First find 1/distance cubed
double dist=sqrt(x*x+y*y);
dist=1.0/(dist*dist*dist);
ax=-x*mg*dist;
ay=-y*mg*dist;

//Do another half timestep like in leapint.c
vx+=ax*dt/2.0;
vy+=ay*dt/2.0;