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Nonhomogenous Second Order DE

  1. Mar 9, 2008 #1
    [SOLVED] Nonhomogenous Second Order DE

    1. The problem statement, all variables and given/known data
    [tex]y'' - 2y' - 3y = -3te^{-t}[/tex]
    Solve


    2. Relevant equations



    3. The attempt at a solution

    Well first I tried
    [tex]Y(t) = Ate^{-t}[/tex]
    then
    [tex]Y(t) = At^2e^{-t}[/tex]
    then
    [tex]Y(t) = At^3e^{-t}[/tex]
    and
    [tex]Y(t) = At^3e^{-t} + Bt^2e^{-t}[/tex]
    but I can't seem to get the correct form.

    Does anyone know what form I need my Y(t) in order to solve this?
     
  2. jcsd
  3. Mar 9, 2008 #2
    I believe I end up with a term like
    [tex]Ae^{-t} = -3te^{-t}[/tex] which I don't believe I can do anything with?

    In fact, in all the cases I've tried I always seem to get something like [tex]Ae^{-t}[/tex] which never cancels out so I can never equation -3te^{-t} to any of my terms
     
    Last edited: Mar 9, 2008
  4. Mar 9, 2008 #3
    ah finally got it with [tex]At^2e^{-1}+Bte^{-1}[/tex]
    bah that sucked
     
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