Answer
$t^2 e^{3t}$
Work Step by Step
Since, $F(s)=\dfrac{1}{(s-3)^2}$
The inverse Laplace transform of function can be expressed as:
$F(s)=\dfrac{1}{s^2}$ and $f(t)=t$
Now, apply the first shifting Theorem.
$f(t)=t^2 e^{3t}$
Differential Equations and Linear Algebra (4th Edition)
by Goode, Stephen W.; Annin, Scott A.
Published by
Pearson
ISBN 10:
0-32196-467-5
ISBN 13:
978-0-32196-467-0
Chapter 10 - The Laplace Transform and Some Elementary Applications - 10.5 The First Shifting Theorem - Problems - Page 695: 28
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