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## Homework Statement

y''-4y'+4y=x*e

^{2x}

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

## Homework Equations

## The Attempt at a Solution

y''-4y'+4y=0

Using the characteristic function:

a

^{2}-4a+4=a <=> (a-2)

^{2}=0

Therefore

C1*e

^{2x}

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!