1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper
    Gold Member

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


    [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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook