# Inverse laplace transform

1. Mar 23, 2012

### schapman22

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:

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• ###### homework5.jpg
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2. Mar 23, 2012

### schapman22

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.

3. Mar 24, 2012

### schapman22

Hey I still cant figure this one out. If anyone has any advice it would be very much appreciated. Thank you.

4. Mar 24, 2012

### LCKurtz

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 $e^t$.