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Homework Help: Dirac Delta function

  1. Jul 3, 2011 #1
    The problem statement, all variables and given/known data
    Solve the given symbolic initial value problem: [tex]y''-2y'-3y=2\delta (t-1)-\delta (t-3) ;y(0)=2,y'(0)=2[/tex]

    The attempt at a solution

    Let Y(s):= L{y(t)}(s)

    Taking laplace transform of both sides:

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

    And my final answer:


    Is this correct?
  2. jcsd
  3. Jul 3, 2011 #2


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    Homework Helper

    It looks to be right sort of thing to be doing.
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