Example 9.13.  Solve  [Graphics:Images/ZTransformDEMod_gr_51.gif]   with  [Graphics:Images/ZTransformDEMod_gr_52.gif].  

[Graphics:Images/ZTransformDEMod_gr_53.gif]

Solution 9.13.

    The characteristic equation  [Graphics:../Images/ZTransformDEMod_gr_54.gif]  has equal roots [Graphics:../Images/ZTransformDEMod_gr_55.gif]  hence the general solution is  [Graphics:../Images/ZTransformDEMod_gr_56.gif].  Use the initial conditions and form the linear system  

        [Graphics:../Images/ZTransformDEMod_gr_57.gif]  

then solve for the constants and get  [Graphics:../Images/ZTransformDEMod_gr_58.gif].  Hence the solution is

        [Graphics:../Images/ZTransformDEMod_gr_59.gif].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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