Answer
True
Work Step by Step
The first shifting Theorem can be expressed as:
When $L[t^3]=\dfrac{ 3!}{s^{3+1}}=F(s)$,
Then we have: $L[e^{2t}t^3]=F(s-2)\\=\dfrac{6}{(s-2)^4}$
Therefore, the given statement is $\bf{True}$.
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 - True-False Review - Page 694: f
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