Example 9.20 (a).  Find the general solution to  .

Solution 9.20 (a).

    The homogeneous difference equation has the form  (9-8) with and   so that the solution are complex and have the form  

        ,  

where    and  .  Hence, the general homogeneous solution is  

        .

Remark.  The homogeneous solution is transient and and will decay to as , i.e.  .  An illustration using is shown in figure 2 below.

Typo.  Please note that there is a typo in the book which mistakenly stated that the homogeneous solution involves .  We apologize for this inconvenience.

(c) 2006 John H. Mathews, Russell W. Howell