# Euler's Method C++ Program For Solving Ordinary Differential Equation

This program is implementation of Euler's method for solving ordinary differential equation using C++ programming language with output.

Output of this is program is solution for dy/dx = x + y with initial condition y = 1 for x = 0 i.e. y(0) = 1 and we are trying to evaluate this differential equation at y = 0.5. ( Here y = 1 i.e. y(0.5) = ? is our calculation point)

## C++ Program for Euler's Method

``````
#include<iostream>

/* defining ordinary differential equation to be solved */
/* In this example we are solving dy/dx = x + y */
#define f(x,y) x+y

using namespace std;

int main()
{
float x0, y0, xn, h, yn, slope;
int i, n;

cout<<"Enter Initial Condition"<< endl;
cout<<"x0 = ";
cin>> x0;
cout<<"y0 = ";
cin >> y0;
cout<<"Enter calculation point xn = ";
cin>>xn;
cout<<"Enter number of steps: ";
cin>> n;

/* Calculating step size (h) */
h = (xn-x0)/n;

/* Euler's Method */
cout<<"\nx0\ty0\tslope\tyn\n";
cout<<"------------------------------\n";

for(i=0; i < n; i++)
{
slope = f(x0, y0);
yn = y0 + h * slope;
cout<< x0<<"\t"<< y0<<"\t"<< slope<<"\t"<< yn<< endl;
y0 = yn;
x0 = x0+h;
}

/* Displaying result */
cout<<"\nValue of y at x = "<< xn<< " is " << yn;

return 0;
}

``````

## Euler's Method C++ Program Output

```Enter Initial Condition
x0 = 0
y0 = 1
Enter calculation point xn = 0.5
Enter number of steps: 10

x0      y0      slope   yn
------------------------------
0.000   1.000   1.000   1.050
0.050   1.050   1.100   1.105
0.100   1.105   1.205   1.165
0.150   1.165   1.315   1.231
0.200   1.231   1.431   1.303
0.250   1.303   1.553   1.380
0.300   1.380   1.680   1.464
0.350   1.464   1.814   1.555
0.400   1.555   1.955   1.653
0.450   1.653   2.103   1.758

Value of y at x = 0.500 is 1.758
```