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Differential equation using laplace

  1. Jan 22, 2007 #1
    1. The problem statement, all variables and given/known data
    How do I solve the following differential equation with the Laplace Transform:?
    f(t)'' - a*f(t) = 0 (all ICs are equal to zero).



    2. Relevant equations



    3. The attempt at a solution

    So, I get something like F(s)*(s^2 - a) = 0. I don't know where to go from there.
     
  2. jcsd
  3. Jan 22, 2007 #2

    Dick

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    Your equation is missing terms which correspond to the boundary behavior of f(t). F(s)=0 is not the only solution.
     
  4. Jan 22, 2007 #3

    Dick

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    Hmmm. If as you say all IC's are 0. f(0)=f'(0)=0. Then f(t)=0 is the only solution. Pretty trivial use of laplace transforms.
     
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