Milne-Simpson's Method for O.D.E.'s PVIs, IVPs

The Milne-Simpson method uses   in the calculation of .  This method is not self-starting;  four initial points  , , ,  and must be given in advance in order to generate the points . 

Mathematica Subroutine (Milne-Simpson's Method).

Example 1.  Solve the I.V.P.  . 
Solution 1.

Example 1.  Solve the I.V.P.  . 

Solution 1.
Compute the Milne-Simpson solution based on 25 subintervals and plot the results.