1. The problem

Consider the difference equation .

What is the

(a)step responsefor the causal system satisfying this difference equation,

(b)general form of the homogeneous solutionof the difference equation?

(c)Consider a different system satisfying the difference equation that is neither causal nor LTI, but that has y[0] = y[1] = 1. Find theresponse of this system to x[n] = [n].

2. Relevant equations and definitions

Oppenheim's definition of(b),the general form of the homogeneous solution:

3. The attempt at a solution

(a)step response, s[n]

I have calculated the impulse response , and put it to use in calculatings[n](where I get stuck):

(b)general form of the homogeneous solution

I have no idea (similar problem as(a)in this question on MHF) ... the solution ought to be .

(c)response of a particular system to x[n] = [n]

Confused as well. I do get particular values fory[n]:

y[-1] = 41/5,

y[0] = 1,

y[1] = 1,

y[2] = 2/3,

...

continuing in this manner (and hoping for a pattern to emerge) surely isn't the way to go?

The solution given is:. Other answers are possible.