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Homework Help: Laplace transforms

  1. Apr 26, 2010 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    Using the laplace transform find the equation.

    3. The attempt at a solution

    I already have a really long answer. . .I was just wondering if someone can explain this:

    Another method (appart from using integration by parts multiple times) was mentioned by my professor, he said to take the partial with respect to s of the integral, which will then just leave the partial laplace transform of cos(t) which can be found trough tables

    I remember he explained it but now that I think about it it doesnt make sense:

    L {t cos(t)} = (int)infinity0 e-stt cos(t)dt
    then you can take the partial with respect to s (d/ds) of that integral, and yo uwould end up with

    d/ds [L{cost}] = d/ds [s/(s^2+1)]

    cans omeone explain?
    I remember he mentioned the potential function
  2. jcsd
  3. Apr 27, 2010 #2


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    Staff Emeritus
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    You use the fact that

    [tex]te^{-st} = -\frac{\partial}{\partial s}e^{-st}[/tex]

    and then switch the order of integration and differentiation.
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