Exercise 20.  Consider the system of difference equations

with the initial conditions   .  

20 (a).  Use trigonometric identities to verify that the solution is      and   .  

Solution 20 (a).

See text and/or instructor's solution manual.

        Given    and    we have

                      

                    and

                      

We are done.   

Aside.  We can let Mathematica double check our work.

          The Maple commands are similar  

  

                                                            


  

                                                            


  

                                                            


  

                                                            

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell