# Find a particular solution for a non-homogeneous differential equation

1. May 3, 2013

### blouqu6

Find a particular solution for the following equation:

y"+2y'+y=12.5e-t

I'm not sure on which method to use. Here's my attempt using the undetermined coefficients method:

→y"+2y'+y=12.5e-t
r2+2r+1=0
r=-1 *not even sure if this part is useful

→yp=e-t
yp'=-e-t
yp"=e-t

→y"+2y'+y=12.5e-t
(e-t)+2(-e-t)+(e-t)=12.5e-t

e-t(1-2+1)=e-t(12.5)

This is where I get stuck; I don't believe I'm taking the right approach from the get-go. Any help would be greatly appreciated.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 3, 2013

### Staff: Mentor

It's very useful, as it gives you the complementary solution, the solution to the homogeneous problem. Note that r = -1 is a repeated solution of the characteristic equation.
Not a good choice for a particular solution. e-t is a solution of the homogeneous problem, so can't possibly be a solution of the nonhomogeneous problem.