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Using Laplace Transforms to solve IVP's

  1. Jan 14, 2009 #1
    1. The problem statement, all variables and given/known data
    solve the ivp using laplace tranforms

    y''+2y'+2y=0 y(0)=1 y'(0)=-3


    2. Relevant equations



    3. The attempt at a solution

    get to Y(s)[s^2+2s+2]=s-1

    Y=(s-1)/[s^2+2s+2]

    ^^^
    don't know how to simplify the denominator to solve using Laplace transforms. If I had to guess I would say maybe partial fractions but keep getting the wrong answer when I try to use them.
     
  2. jcsd
  3. Jan 14, 2009 #2
    You've pretty much finished it, all you need to recognize that

    [tex] Y(s)=\frac{s-1}{(s-1)^2+1}[/tex]

    through completing the square in the denominator. Now can you get that to work with

    [tex]f(t)=L^{-1}\left\{\frac{s-a}{(s-a)^2+b^2} \right\} = e^{at}\cos{(bt)}[/tex]
     
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