Undetermined Coefficient with repeated roots

[Ian88]

Homework Statement

The problem is: y" + 2y' - 3y = x^2*e^x

Homework Equations

The Attempt at a Solution

I know the roots are y1 = -3 and y2 = 1, becoming e^x.

I'm not sure how to set my yp up though with the repeating e^x.

My ideas are yp = x * (x^2*A*e^x) or x * (Ax^2 + Bx + C)e^x.

I was also curious on the setup of a problem where yp = P(x)*e^ax* cos(bx).

 

[rock.freak667]

since '1' is a root, the PI for e^x is xe^x, and PI for x² is Ax²+Bx+C, so put those 2 together

y_p=xe^x(Ax²+Bx+C)