Undetermined coefficient method

[masterchiefo]

Homework Statement

y''+10y'+25y=x+2+3e^-5*x

Homework Equations

The Attempt at a Solution

F(D) = D²+10D+25 zeroes: -5
yc= C1*e^-5*x + C2*e^-5*x *x

yp = ax+b + C*e^-5*x
yp = ax+b + C*e^-5*x*x²

I just want to know if my yc and yp is correct, after that I know how to do it.

 

[HallsofIvy]

yc is correct, yp is not. The SECOND yp, $ax+ b+ cx^2e^{-5x}$ is correct. Since $e^{-5x}$ and $xe^{-5x}$ satisfy the associated homogenous equation you need the "$x^2$".