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Inverse laplace transform

  1. Mar 23, 2012 #1
    1. The problem statement, all variables and given/known data

    Having found the laplace transform of a differential equation. I must now find X(t). All of my work is attached. The problem I am having is fitting my function of s to my table of transforms. I tried using partial fractions but it took me in a loop.


    3. The attempt at a solution

    I attached everything.
     

    Attached Files:

  2. jcsd
  3. Mar 23, 2012 #2
    I know the answer is et which means somehow 1/(s-1)2 becomes 1/(s-1). But I don't understand how to get rid of the other (s-1) in the denominator.
     
  4. Mar 24, 2012 #3
    Hey I still cant figure this one out. If anyone has any advice it would be very much appreciated. Thank you.
     
  5. Mar 24, 2012 #4

    LCKurtz

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    I have trouble reading your images, but if you are trying to inverse ##\frac 1 {(s-1)^2}## you can use one of the shifting theorems$$
    \mathcal L^{-1}f(s-a) = e^{at}\mathcal L^{-1}f(s)$$Do you see how to use that? Your answer isn't just ##e^t##.
     
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