Example 2.  Consider the D. E.    over    with    and  .
Use the "linear shooting" method and solve for the first function u(t).  

Solution 2.

Enter the function  p(t), q(t) and r(t) into Mathematica.  

The method involves solving a two systems of equations over  ,  

First solve     
                            with    ,  
        and    .  
For the latter equation use the function

Send this to the Runge2D subroutine.

The first solution we obtain is u.

Now we can plot the solution.

(c) John H. Mathews 2004