Example 9.17 (a).  Use z-transform methods to solve     with  .  

Solution 9.17 (a).

Take the z-transforms of each term  

        

Solve for   and get  

Calculate the residue for    at the poles
    
          

          

Therefore, the solution is  

        

        

which agrees with the result of example 3.

Remark.  Observe that .

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