Consider the difference equation:
y(n)=(5/6)y(n-1) - (1/6)y(n-2) + x(n)
where x(n) = 2^n u(n)
and y(n) = 0 for all n < 0.
(i) Calculate the homogeneous solution.
(ii) Calculate the zero-input solution.
(iii) Derive the zero-state solution.
(iiii) Derive the total solution.
(iiiii) Verify that the total solution = zero-input solution + zero-state solution.
(iiiiii) Derive the impulse response.