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Help with differential equation

  1. Aug 2, 2009 #1
    Solve with convolution integral:

    Click http://i3.photobucket.com/albums/y62/Phio/eq.jpg" [Broken] to see the equation.

    So far what I've got is http://i3.photobucket.com/albums/y62/Phio/attempt.jpg" [Broken]. I don't know what else to do from there, or if what i'm doing is right...


    Any help appreciated!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 3, 2009 #2

    gabbagabbahey

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    First, [itex]c_3[/itex] should be equal to [itex]k[/itex] from your DE should it not?

    Second,

    [tex]X(s)=\frac{F(s)}{s^2+k}+\frac{c_1s}{s^2+k}+\frac{c_2}{s^2+k}\implies x(t)=\mathcal{L}^{-1} \left\{ \frac{F(s)}{s^2+k}+\frac{c_1s}{s^2+k}+\frac{c_2}{s^2+k} \right\}[/tex]
    [tex]=\mathcal{L}^{-1} \left\{ \frac{F(s)}{s^2+k} \right\}+\mathcal{L}^{-1} \left\{ \frac{c_1s}{s^2+k} \right\}+\mathcal{L}^{-1} \left\{ \frac{c_2}{s^2+k} \right\}[/tex]

    You shouldn't have much trouble doing the last two inverse Laplace transforms, and the first one can be done using the convolution rule....
     
  4. Aug 3, 2009 #3
    Oooh I thought about that...this helps!

    Thanks a lot!
     
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