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Laplace Transform (Should be easy)

  1. Mar 31, 2008 #1
    [SOLVED] Laplace Transform (Should be easy)

    1. The problem statement, all variables and given/known data
    I know there are other ways to solve this, but I HAVE to use Laplace Transform

    y''-y'-6y=0 where y(0)=2 and y'(0)=-1

    3. The attempt at a solution

    Written as Laplace:


    [tex]\Rightarrow s^2*Y(s)-s*y(0)-y'(0)-s*Y(s)+y(0)-6*Y(s)=0[/tex]

    [tex]\Rightarrow s^2*Y(s)-2s+1-s*Y(s)+2-Y(s)=0[/tex]

    [tex]\Rightarrow s^2*Y(s)-s*Y(s)-Y(s)=-3+2s[/tex]

    [tex]\Rightarow Y(s)=\frac{-3+2s}{s^2-s-1}[/tex]

    Am I missing something? The numerator and denominator don't factor. Is a separation by partial fractions my next step? Or did I miss something that would make it way easier?

  2. jcsd
  3. Mar 31, 2008 #2


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    Staff Emeritus
    Science Advisor

    What happened to the "6" on 6Y(x)?

    s2- s- 6 certainly does factor!
  4. Mar 31, 2008 #3
    Splendid!! Now too bad the numerator wasn't -3+s then I would be in business.
  5. Apr 2, 2008 #4
    I'm also having a problem with laplace transforms.

    I have an equation in the form

    I = [tex]\frac{1}{s}[/tex] - [tex]\frac{11}{3s+2}[/tex]

    Does this transform to

    I(t) = 1-11[tex]e^{-2t}[/tex]

    or do i need to try and do something with the 3?

    I think I just got it, sorry for hi-jacking you're thread.
    I(t) = 1 - 11/3 ([tex]e^{-2/3t}[/tex])
    Last edited: Apr 2, 2008
  6. Apr 2, 2008 #5

    It's cool. And you got it right it looks like!
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