What do your notes give you in terms of formulae and theorems for this kind of problem?
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?
Find pn for the constant part
Combine pn and bn
Sub in initial conditions and solve for constant variables in pn
Where i'm at with finding pn
4( ((-An-1)(B(n-1)-C) + ((-An-1)(C(n-1)-D)(E2n-1)) ) + 5 ( ((An-2)(B(n-2)-C) + ((-An-2)(C(n-2)-D)(E2n-2)) ) + (-1)n(36n - 6) + ( (-1)n(11n - 10) / 2n )
But I have no clue if that's the right direction.