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Homework Help: Laplace Transform

  1. Mar 14, 2009 #1
    1. The problem statement, all variables and given/known data

    y''+y = f(t)

    y(0) = 0; y'(0)=1

    f(t) = 1, 0<=t<pi/2
    0, pi/2<=t


    3. The attempt at a solution
    so far, i have


    (s^2+1)*L{y} = [tex]\frac{s-e^(-pi/2s)}{s}[/tex] +1

    what is next ?
     
  2. jcsd
  3. Mar 14, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    That doesn't look quite right; the Laplace Transform of [itex]f(t)[/itex] is not [tex]\frac{s-e^{-\pi s/2}}{s}[/tex] (although it's close). Double check that calculation.

    Once you correct your expression, solve for [itex]\mathcal{L}[y(t)][/itex] and then take the inverse Laplace transform to get [itex]y(t)[/itex]
     
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