Method of undetermined coefficients question

[illidari]

Homework Statement

y''+y'=g(x)
fundamental set of solns. of the homog. DE is:
y1= 1 , y2= e^-x

If g(x) = x^2 , yp1 = ____

Homework Equations

The Attempt at a Solution

I actually am looking at a key to an old test my teacher gave as a review for a test. The key has the asnswer as x(Ax^2+Bx+C)

Is there any reason why the x was added? Shouldn't it only be (Ax^2+Bx+C). Much thanks if someone can clarify this for me.

 

[frozenguy]

I'm pretty sure its because when you're finding your particular solution, you can't start with terms that duplicate terms in the fundamental set. Since you have a constant as a solution in the fundamental set, you need to multiply the particular solution by x (because of C).