Using Euler's Method to solve Ordinary Differential Equations (Numerical Analysis Using C++)

The velocity of a freely falling object near Earth's surface is described by the equation eq. 1

Eq 1

where is the velocity and g = 9.8 m/s^2 is the acceleration due to gravity. Write a program that employs the Euler method to compute the solution to Equation 1; that is, calculate v as a function of t. For simplicity assume that the initial velocity is zero --that is, the object starts from rest-- and calculate the solution for times t=0 s to t=10 s. Repeat the calculation for several different values of the time step, and compare the result with the exact solution to Equation 1. It turns out that for this case the Euler method gives the exact result. Verify this with your numerical results and prove it analytically. Please write the program in C++ and include many comments and explanatory notes which explain the reasoning behind the construction and structure of your source code.

b = du