So I have an assignment and i'm having trouble doing it. The question in hand.
1. a) Solve the recurrence relation:
an = 4an-1 + 5an-2 + (-1)n(36n - 6) + ( (-1)n(11n - 10) / 2n )
where a0 = 1 and a1 = 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.
an = 4n-1 + 5an-2
x2 -4x - 5
(x - 5)(x + 1)
bn = C15n + C2(-1)n
b) Write down the close form of the generating function of the sequence an.
Maybe a hint to which direction I should go?