I have the following equation:
$$\frac{Z-1}{{Z^2}-2Z+6}$$
I tried to apply difference equation on it:
$$y_{n+2}-5y_{n-1}-6y_n = x_{n+1}-x_n$$
I need to find equation expressed as $y_n$
I have the answer (At the end of the chapter) to be: $$y_n = 5y_{n-1}-6y_{n-2}+x_{n-1}-x_{n-2}$$
Can somone please tell me how did in this case the second equation expressd as $y_n$ ? I cant figure it out!
The differences between your equation and the book's are:
the index has been shifted by 2
the sign on the 6 has been corrected
two terms have been moved to the other side
To see the index shift, define $m=n+2$ and substitute it in.
Also, the $2$ in the denominator has become $5$ in both your solution and the book's. Did you copy it correctly?