# Undetermined coefficient method

1. Oct 17, 2015

### masterchiefo

1. The problem statement, all variables and given/known data
y''+10y'+25y=x+2+3e-5*x

2. Relevant equations

3. 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.

2. Oct 17, 2015

### 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 "$x^2$".