# Thread: Non-homogeneous recurrence relation (form question)...

1. ## Non-homogeneous recurrence relation (form question)...

Consider 2an = 7an-1 - 3an-2 + 2n.

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: 2an = 7an-1 - 3an-2.

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

Characteristic: x2 = 7x - 3.

Or...

Homogeneous: an = (7/2)an-1 - (3/2)an-2.

Characteristic: x2 = (7/2)x - (3/2).

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

2. ## Re: Non-homogeneous recurrence relation (form question)...

$2x^2=7x-3$?
Then, you have $2x^2-7x+3=0 \Longrightarrow (2x-1)(x-3) = 0$, $x=\dfrac{1}{2}$ or $x = 3$.