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Laplace transforms of a reciprocal derivative.

  1. Nov 22, 2012 #1
    1. The problem statement, all variables and given/known data

    The problem basically asks to solve the system

    [itex]x'(3x-1)=36e^{6t}[/itex]

    by using laplace transforms.


    3. The attempt at a solution

    I've started by writing it

    [itex] (3x-1) = \frac{36e^{6t}}{3x-1}[/itex]

    then applying laplace transform to the left side is quite simple, we get 3X(s) - 1/s.

    As for the right hand side, I've fiddled with the identity L[eatf(t)] = F(s-a), I get:

    Let [itex] \frac{1}{x'} = f(t) [/itex] then [itex]36L[e^{6t}f(t)]=36F(s-6)[/itex]

    But then I need to try and find F(s) so that [itex] L^{-1}(F(s)) = \frac{1}{x'} [\itex] and I'm stuck.

    What do?
     
  2. jcsd
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