# Differential equation root

1. Mar 28, 2012

### Jalo

1. The problem statement, all variables and given/known data
y''-4y'+4y=x*e2x

I'm trying to find the homogenous solutions of this equation. I know there are two, but I can only find one.

YH=> y''-4y'+4y=0

2. Relevant equations

3. The attempt at a solution

y''-4y'+4y=0
Using the characteristic function:
a2-4a+4=a <=> (a-2)2=0
Therefore
C1*e2x
is a solution. However, since this is a 2nd order differential equation, I should have two. I can solve the rest of the equation if I can find the 2nd solution. I've tought about it a lot but can't manage to find the answer... All help will be appreciated.
Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Mar 28, 2012

### Dick

If you have a double root 2, then C2*x*e^(2x) is also a homogeneous solution.

Last edited: Mar 28, 2012