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Homework Help: Explicit check for Laplace transform?

  1. Jan 14, 2016 #1
    1. The problem statement, all variables and given/known data
    Solve the following initial value problem using Laplace transforms: y' + 4y = 3t3 e−4t ; y(0) = 0 . Useful information: Recall that the Laplace transform of y 0 is pY − y(0), where Y is the Laplace Transform of y. The Laplace transform of tk e−at is k!/(p + a)k+1 . Confirm the validity of your result by an explicit check.

    2. Relevant equations
    tk e−at is k!/(p + a)k+1

    3. The attempt at a solution
    So I have the solution:

    y=3/4 t4e−4t

    And I know this is correct.

    However is there a specific check I can do to make sure this is correct? ie. What is the explicit check?
  2. jcsd
  3. Jan 14, 2016 #2


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    If you understand what a differential equation is, the specific check you could do becomes self-evident.

    Said differently: you claim to have the solution. What does it mean that y=3/4 t4e−4t is the solution?
  4. Jan 14, 2016 #3

    Ray Vickson

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    Suppose somebody gave you the alleged solution ##y = (3/4) t^4 e^{-4t}## but did not tell you where it came from; how could you check if it is correct?
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