Example 1.  Consider the D. E.    over    with    and  .
Is this a "linear differential equation" ?  Why ?
Identify the functions p(t), q(t) and r(t).  

Solution 1.

Look at the given D.E. and see how it is related to the form given in the theorem.

      with      

Our problem is seen to be

     with    and  .  

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

Notice that q(t) is negative over the interval. Don't worry, the solution    can be computed with  .  

(c) John H. Mathews 2004