I have been reading the recent difference equation post and a question occurred to me. (Please forgive me I know many techniques but little theory for linear algebra.)

I know how to solve something like

$\displaystyle a_{n + 2} - 3a_n = 2$

But what about

$\displaystyle na_{n + 2} - 3a_n = 0$

for example. Is there a general method to attack something like this?

(I don't know if this even has a "nice" solution, I'm just using it as a sample equation where one or more of the coefficients depends on n.)

-Dan