Laplace transform of (e^-s) / [ (s)(s-3) ]

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Homework Statement



find the laplace transform of (e^-s) / [ (s)(s-3) ]

since there's (e^-s) which can be found in L { f(t-a) H(t-a) } = (e^-(as)) F(s) , so , i found a = 1 , then i found F(s) = 1/ [ (s)(s-3) ] , formula :
HGbjXV9.jpg


i have attached the working below , is it correct ? btw , the author's ans doesnt have H(t-a) , is the author's ans wrong ?
author's ans :

2v2kPyD.jpg


Homework Equations




The Attempt at a Solution


my working :
AD0HQrk.png


which is correct ? the author ? or me ?
 
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Answers and Replies

  • #2
Ray Vickson
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Homework Statement



find the laplace transform of (e^-s) / [ (s)(s-3) ]

since there's (e^-s) which can be found in L { f(t-a) H(t-a) } = (e^-(as)) F(s) , so , i found a = 1 , then i found F(s) = 1/ [ (s)(s-3) ] , formula :
HGbjXV9.jpg


i have attached the working below , is it correct ? btw , the author's ans doesnt have H(t-a) , is the author's ans wrong ?
author's ans :

2v2kPyD.jpg


Homework Equations




The Attempt at a Solution


my working :
AD0HQrk.png


which is correct ? the author ? or me ?
There is no way that an author would have asked you to find the Laplace transform of ##e^{-s}/(s(s-3))##. Are you sure it does not ask for the INVERSE Laplace transform? There is a huge difference between these two concepts.
 

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