I would like some help solving this differential equation if possible:
y'' + 2y' + y = xe^(-x)
I end up with the complementary solution of the equation being:
y = C1*e^(-x) + C2*xe^(-x) + yp
However, here I get stumped for how to solve for yp. I set the trial solution as (Ax+B)e^(-x) and then differentiat to find y' and y'' and plug it into the equation. But then everything cancels out giving me x = 0.
Can someone explain how to solve the rest of this?