Example 7.  Consider a drum head of radius . For convenience, choose the parameter  . The method of separation of variables permits us to use the substitution  .  Use this substitution and obtain the D.E.
    .      
Solve this D.E. and plot the solution over the interval  .
Solution 7.

The solution we require is the one involving the function  .
For illustration, set    and graph  .

Aside. The function   is not the one we use because it has goes to when    
For illustration, set    and graph  .

(c) John H. Mathews 2004