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Laplace is hurting my brain

  1. Apr 18, 2004 #1
    OK, here's the problem

    [tex]L^{-1}\{\frac{s}{s^2+4s+5}\}[/tex]

    What I did:
    [tex]L^{-1}\{\frac{s}{(s+2)^2+1}\}[/tex]

    [tex]=e^{2t}\cos{t}[/tex]

    The book says:
    [tex]=e^{2t}\cos{t}-2e^{2t}\sin{t}[/tex]


    Where did the [itex]2e^{2t}\sin{t}[/itex] come from?

    Mahalo.
     
  2. jcsd
  3. Apr 18, 2004 #2
    Mathematica is saying that it's neither of those...

    cookiemonster
     
  4. Apr 18, 2004 #3

    turin

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    Homework Helper

    The cannonical form has an (s+2) in the numerator, not just s (so your invesrse transform calculation was actually incorrect). In order to account for that, you have to add another rational function that has a numerator of -2, which just happens to be (-2) times the cannonical form with sin instead of cos.
     
  5. Apr 19, 2004 #4
    Thanks a lot. I missed about a month of Diff Eq due to illness and an auto accident so I've been learning it all on my own. I appreciate the Q&A forum here and all those who help out.
     
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