//this code has to solve the equation y'= f(x,y) where f(x) is given in the function. but there is some error in the solution. correct it by changing only one line.
# include <stdio.h>
# include <math.h>
#include<iostream.h>
#include<conio.h>
#include<iomanip.h>
 double f(double a, double b)
                  {
                  double function;
		  function = -b+a+1;
                  return(function);
		  }
 double f(double a)
                  {
		  double function;
		  function =exp(a);
                  return(function);
		  }
 int main()
  {
   int N=10;
  int i=0;
  double a=0,b=1;
  double h=(b-a)/N;
  double t,y,py,y0=1;
  double y1;
  cout<< "\nEuler's method for solving y'= f(x,y) with step size "<<h<<"\n";
  cout<<"i\tt\t\t y(i+1)\t\tp(i+1)\t\texact sol\n";
		  t=a;
		  y=py=y0;
		  while (i <= N)
		  {
		     y=y+h*f(y,t);
		     py=py+(h/2)*(f(t,py)+f(t+h,y));
		     y1=f(t);
		     cout<<i<<"\t"<<setiosflags(ios::showpoint)<<setprecision(4)<<t<<"\t\t"<<setprecision(6)<<y<<"\t"<<py<<"\t"<<setiosflags(ios::fixed)<<y1<<"\n";
		     i++;
		     t=t+h;
		   }
	    getch();
return 0;
}