So I have an assignment and i'm having trouble doing it. The question in hand.

1. a) Solve the recurrence relation:

a_{n}= 4a_{n-1}+ 5a_{n-2 }+ (-1)^{n}(36n - 6) + ( (-1)^{n}(11n - 10) / 2^{n})

where a_{0 }= 1 and a_{1}= 0.5

I got as far as to find the characteristic solution for the homogeneous part but have no clue how to find the particular solution for the next part.

a_{n}= 4_{n-1}+ 5a_{n-2}

x^{2}-4x - 5

(x - 5)(x + 1)

b_{n}= C_{1}5^{n}+ C_{2}(-1)^{n}

b) Write down the close form of the generating function of the sequence a_{n. }Maybe a hint to which direction I should go?

Thank you!