# Thread: help with difference equations

1. ## help with difference equations

Hello. So I am currently having problems with difference equations. The problem is:
$a[n] + 2a[n-1] = n$.

I am not sure where to begin. I'm not asking for an answer I just want to know what I need to do. I have tried looking up tutorials and such but they all seem very complicated. There is another problem I solved somewhat similar and I have attached my work.

Any help would be appreciated.

Thanks,

Jimbo

2. In this case there is only one root r, the characteristic equation is given by
the sum from k=0 to N of (a_k)(r^N-k)=0 where N=1 and a_k represents the coefficients e.g a_1=2
Find r and then write down the solution as in your previous example.
Hope this helps...

3. Originally Posted by jbm715
Hello. So I am currently having problems with difference equations. The problem is:
$a[n] + 2a[n-1] = n$.

I am not sure where to begin. I'm not asking for an answer I just want to know what I need to do. I have tried looking up tutorials and such but they all seem very complicated. There is another problem I solved somewhat similar and I have attached my work.

Any help would be appreciated.

Thanks,

Jimbo
Try letting

$a_n = b_n + pn + q$

and choose $p$ and $q$ (constants) to transform your problem to

$
b_n + 2 b_{n-1} =0.
$