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Laplace transform

  1. May 14, 2009 #1
    I need to find the laplace transform of
    y''(t)-y(t)=0 with initial conditions y(0)=1 and y'(0)=3

    My attempt:
    Ly''(t)=(s^2)F(s)-s(1)-(3)
    Ly'(t)=sF(s)-1
    so (s^2)F(s)-s(1)-(3)-sF(s)-1=0
    I need to isolate F(s) so
    F(s)=-(2/s^2)
    Is this correct?
     
  2. jcsd
  3. May 14, 2009 #2

    Cyosis

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    Homework Helper

    You're solving for a different differential equation than the one you have listed. You are solving [itex]y''(t)-y'(t)=0[/itex]. That said you still made some mistakes. Your first two steps are correct, but then when you subtract the two you make a minus sign error. It should be,

    [tex]s^2 F(s)-s-3-(s F(s)-1)=s^2 F(s)-s-3-sF(s) \textcolor{red}{+} 1=0[/tex].

    I am not sure how you isolated the F(s), something seems to have gone wrong there as well. You can write it like,

    [tex](s^2-s)F(s)-(s+2)=0[/tex]
     
  4. May 14, 2009 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You wrote the problem as y"- y= 0, but you solved y"- y'= 0.
     
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