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Homework Help: Differential Equation - Inverse Laplace Transformation

  1. May 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the inverse laplace transformation of [tex]\frac{2s^2 +3s - 2}{s(s+1)(s-2)}[/tex]

    2. Relevant equations

    3. The attempt at a solution

    [tex]L^{-1} \frac{2s^2 +3s - 2}{s(s+1)(s-2)} = L^{-1}\frac{1}{2} + L^{-1}\frac{1}{s+1} +2 L^{-1}\frac{1}{s-2} = 1 - e^{-t} + 2e^{2t}[/tex]

    Have I made a mistake somewhere?

    and does anyone know where I can find a web site practice problems (preferably with answers so I can check) similiar to this one?
  2. jcsd
  3. May 13, 2009 #2


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    Homework Helper
    Gold Member

    Assuming that the [itex]\mathcal{L}^{-1}[\frac{1}{2}][/itex] was just a typo, and you meant to write [itex]\mathcal{L}^{-1}[\frac{1}{s}][/itex], then yes, you are correct.

    As for practice problems and solutions, a quick Google search came up with http://ece.olin.edu/dynamics/handouts/ogata_ch2_examples_practice.pdf [Broken]. I haven't checked the contents for correctness, but there are several worked problems in there (and I'm sure you can find more yopurself with Google!).
    Last edited by a moderator: May 4, 2017
  4. May 13, 2009 #3
    Yea, I meant to write 1/s.

    Thanks for the link.
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