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Nonhomogenous 2nd order DE

  1. Mar 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Well I've got another one that totally sucks.
    [tex]y'' + 2y' + 5y = 4e^{-t}cos(2t)[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I tried Y(t) = [tex]Ae^{-t}cos(2t) + Be^{-t}sin(2t)[/tex] but that unfortunately yielded [tex]0 = 4e^{-t} cos(2t)[/tex]

    So my question is how does one modify Y(t) in this type of situation? The only thing I can think of is something like [tex]Y(t) = Ae^{-t}t^2cos(2t) + Be^{-t}tsin(2t)[/tex] but that seems rather painful
  2. jcsd
  3. Mar 9, 2008 #2


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    Y(t) = Ae^{-t}tcos(2t) + Be^{-t}tsin(2t)
    which is what you wrote down but I changed a t^2 to a t. Yeah, it's kind of painful, but it will work. Without the t's it just the homogeneous solution. You knew that would give you zero, right?
    Last edited: Mar 9, 2008
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