Struggling to Find X(t) Using Inverse Laplace Transform

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Homework Help Overview

The discussion revolves around finding the inverse Laplace transform of a function derived from a differential equation. The original poster is struggling to match their function of s to known transforms and is specifically dealing with the expression involving 1/(s-1)².

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use partial fractions but encounters difficulties. Some participants question the method of simplification and the application of shifting theorems in the context of inverse Laplace transforms.

Discussion Status

Participants are actively engaging with the problem, with some offering guidance on the use of shifting theorems. There is an acknowledgment of the complexity involved in simplifying the expression, and multiple interpretations of the approach are being explored.

Contextual Notes

There are mentions of difficulties in interpreting attached images, which may affect the clarity of the problem setup. The original poster's understanding of the relationship between the transforms and their inverse is under scrutiny.

schapman22
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Homework Statement



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.

The Attempt at a Solution



I attached everything.
 

Attachments

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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.
 
Hey I still can't figure this one out. If anyone has any advice it would be very much appreciated. Thank you.
 
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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