2 Show the work required to establish Equations 4.608 through 4.610 in part (b) and Equations 4.613 through 4.615 in part (c) of Example: A discrete-time system is described by the difference equation...

2 Show the work required to establish Equations 4.608 through 4.610 in part (b) and Equations 4.613 through 4.615 in part (c) of Example: A discrete-time system is described by the difference equation
Initial conditions y–1 = y–2 = 0. The input sequence is given by
Find the z-domain transfer function H(z) and its poles, the impulse response h_k, k = 0, 1, 2, 3, …, the total response y_k, k=0, 1, 2, 3, …, and the natural and forced components of the total response, and comment on stability for the following cases: