#include<stdio.h>
#include<math.h>
main()
{
   double x,y,yh,dx,exact,gosa;
   y=0.0;
   x=0.0;
   dx=0.1;
   while(x<0.6){
      exact=sin(x)/cos(x);
      gosa=fabs(exact-y);
      printf("x=%4.1lf y=%14.7e exact=%14.7e error=%14.7e\n",x,y,exact,gosa);
      yh=y+dx*(1.0+y*y);
      y=y+dx*((1.0+y*y)+(1.0+yh*yh))/2.0;
      x=x+dx;
   }
   return(0);
}