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Finding Laplace transform of a Differential Equation

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider the following initial value problem:

    y''-6y'-7y=sin(9t)

    y(0)=-4, y'(0)=-3

    I need to solve for L[y(t)]


    2. Relevant equations



    3. The attempt at a solution

    Here are the steps I've taken to solve it:

    L(y'')-6L(y')-7L(y)=L(sin(9t))

    s2L(y)-(-4)-(-3)-6(sL(y)-(-4))-7L(y)=9/(s2+81)

    L(y)(s2-6s-7)-17=9/(s2+81)

    L(y)(s2-6s-7)=9/(s2+81)+17

    Y(s) =((9/(s2+81))+17)/(s2-6s-7)

    I've simplified it with partial fractions as well but either way when I enter it into my homework page it says it's wrong.
     
  2. jcsd
  3. Apr 19, 2012 #2
    Not sure if the work is correct but you have to inverse the Laplace transform at the to solve.
     
  4. Apr 21, 2012 #3

    vela

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    Recheck your Laplace transform of y''.
     
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