Exercise 19.  Consider the system of difference equations

with the initial conditions   .  

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

Solution 19 (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