Implement Eulers method to solve an ordinary differential equation for an arbitrary real-valued function f(x, y) as the right hand side over the interval [0, b]. We wish to approximate the solution to the ordinary differential equation: y 0 = f(x, y) y(0) = y0 using Eulers method and N subintervals. Your program should take four command line arguments: a double representing y0, a double representing the endpoint b, an integer N for the number of subintervals, and the name of an output file into which to write the pairs (xi , yi), with one pair per line, with xi and yi separated by a space.

The function f will be declared in the header file ex1_f.h and defined in the ex1_f.cpp. You will need to #include "ex1_f.h in your main routine. The exact header file and an example of what the corresponding .cpp file might look like are given.

In header file:

#ifndef HW_6_EX_1_F_H #define HW_6_EX_1_F_H double f(double x, double y); #endif 

example .cpp file:

#include "hw_6_ex_1_f.h" double f(double x, double y){ return x * y; }