# Thread: non homogeneous recurrence relations :(

1. ## non homogeneous recurrence relations :(

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?

Thank you!

2. ## Re: non homogeneous recurrence relations :(

Hey ineedalottahelp.

What do your notes give you in terms of formulae and theorems for this kind of problem?

3. ## Re: non homogeneous recurrence relations :(

Originally Posted by chiro
Hey ineedalottahelp.

What do your notes give you in terms of formulae and theorems for this kind of problem?
Basically they've told us to find bn
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.

4. ## Re: non homogeneous recurrence relations :(

I don't know what you're note say, so I can't really comment any further.