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Homework Help: Laplace Transforms with IVP and linear first ODE

  1. Apr 19, 2010 #1
    1. The problem statement, all variables and given/known data
    y'' + ty' - y = 0

    plugging in the known Laplace formuals i get this....
    [s^2Y(s) - sy(0) - y'(0)] + [-sY'(s) - Y(s)] - Y(s) = 0

    2. Relevant equations

    y(0) = 0
    y'(0) = 3

    3. The attempt at a solution
    simplying to a linear first order DE
    -sY'(s) + (s^2-2)Y(s) = 3

    Y'(s) + [(s^2-2)/-s]Y(s) = 3

    now, according to my text book "P(x)" = [(s^2-2)/-s], and i need to find the integrating factor by integrating P(x)

    use e^(p(x)) then etc.

    the problem im having is how to approach integrating p(x). i tried dividing each term by s and integrating them separately but plugging them into e causes hectic problems.

    is there a different way to approach this?
  2. jcsd
  3. Apr 19, 2010 #2


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    Homework Helper
    Gold Member

    I think you have an extra [itex]-Y(s)[/itex] in here.

    Ermm...you mean [itex]P(s)[/itex] right?:wink:

    That's the correct approach...what do you get when you do this (after correcting your 1st error)?
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