Consider 2a_{n}= 7a_{n-1}- 3a_{n-2}+ 2^{n}.

Writing down the associated homogeneous recurrence relation (to this non-homogeneous one) and the characteristic equation... does it matter which of the following I choose?

Homogeneous: 2a_{n}= 7a_{n-1}- 3a_{n-2}.

I'm guessing 2a_{n}still makes a valid homogeneous recurrence relation (for whatever reason?) and doesn't strictly have to be of the form... "a_{n}= ... ".

Characteristic: x^{2}= 7x - 3.

Or...

Homogeneous: a_{n}= (7/2)a_{n-1}- (3/2)a_{n-2}.

Characteristic: x^{2}= (7/2)x - (3/2).

Yes, I want to know 'cause obviously the first form won't be as ugly to solve.