Differential equation root

  • Thread starter Jalo
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  • #1
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Homework Statement


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

Homework Equations





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!

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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If you have a double root 2, then C2*x*e^(2x) is also a homogeneous solution.
 
Last edited:

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