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Math Help - Laplace transforms? Inverse?

  1. #1
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    Laplace transforms? Inverse?

    Hey:

    In my tutorial question, I firstly had to prove that the Laplace transform of a differential equation was:

    L(t) = n!(s-1)^n
    ---------
    s^n+1

    This I have proved, now I need to find the Laplace transform of t*L(t) and then have to deduce the value of:

    Integral between 0 and inf of : e^-2t * t*L(t)

    I'm really stuck, sorry I can't do the Laplex stuff, hope you can understand it.
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  2. #2
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    Re: Laplace transforms? Inverse?

    this question doesn't make any sense
    rephrase it and then I might be able to help you
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  3. #3
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    Re: Laplace transforms? Inverse?

    You're right, I missed out the first part..

    We start with the differential equation.

    t f ''(x) + (1-t)f ' (x) +nf = 0

    You first had to take the laplace transform of that and prove L(t) above, which i did., now I need to do t L(t), I presume you times this by t and do the same process?
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  4. #4
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    Re: Laplace transforms? Inverse?

    what you're calling L(t) has no t in it...
    plus what do you mean by f(x)?
    I assume you mean f(t) instead?
    think about what you're going to say and I might help
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  5. #5
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    Re: Laplace transforms? Inverse?

    if F(s) is the laplace transform of f(t) then there is an identity that says:

    the laplace transform of t*f(t) is -F'(s)

    using this identity and the integral definition of the laplace transform (with s=2) I think you should be able to solve your problem. That is if I have guessed the problem correctly.
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