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Homework Help: Laplace Transformation, Translation Property

  1. Dec 6, 2009 #1
    Can anyone do a very comprehensive breakdown of the Laplace translation property for me? I don't understand how to apply it:
    L[eat f(t)] = L[f(t)] s-> s-a

    Here is a specific problem that applies it:

    1. The problem statement, all variables and given/known data

    Y(s) = 4/(s+1)3 + 1/(s+1)2 + 2/(s+1)

    I need to perform an inverse Laplace transform to find the solution to this initial value problem (beginning parts of the problem omitted).

    2. Relevant equations

    L[eat f(t)] = L[f(t)] s-> s-a

    3. The attempt at a solution

    let E = (s+1);
    L-1 (4/E3 + 1/E2 + 2/E) = 2t + t + 2

    y(t) = 2t2e-t + te-t + 2e-t

    ... but why?
  2. jcsd
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