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Math Help - solving differential equations using laplace! simple problem

  1. #1
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    Exclamation solving differential equations using laplace! simple problem

    Hello i am trying to solve a differential equation using Laplace transforms...but i am stuck in a very simple step...

    I am stuck in one point of the problem, where i am supposed to make a fraction simplifying...

    i know this is very basic mathematical knowledge, BUT I CANNOT SEE ANY SIMPLIFYING!!!

    Please help me on this!!! can you see any simplification on these fractions??? :

    L[y] (2 s^2 + 2s - 4 ) = 10/s^2 - 15/s + 10s/2

    PLEASE HELP IM SO DESPERATE!!!


    (L[y] is the laplace transform of y of course)
    Last edited by superman83; January 4th 2010 at 06:18 AM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Note:

    2s^2 +2s - 4 = 2(s+2)(s-1)


    L(y) = 5/{(s^2)(s+2)(s-1)} -15/{2s(s+2)(s-1)} + 5 s/(s+2)(s-1)

    If you know convolution the first and second are fairly simple and the 3rd can be found on any table

    See attachment

    Otherwise use a partial fraction decomposition on the first and second
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