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Homework Help: Write a 2nd order DE given two particular solutions

  1. Sep 20, 2011 #1
    The question is:

    Find a second order linear equation which has y1=-3e^(2t) and y2=e^(2t)+2te^(2t) as two of its particular solutions.

    Attempt at a solution:

    Since it's a repeated root problem, we know r=2, therefore the characteristic equation must look like (r-2)^2=0

    r^2-4r+4=0 ----------------------- > y''-4y'+4y=0

    Is this problem really that easy? I have a feeling I'm misinterpreting the question cause this is way too trivial.
  2. jcsd
  3. Sep 20, 2011 #2


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    Science Advisor
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    Gold Member

    Yes, it is that easy. Enjoy it. :smile:
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