a) Find the Laplace transform of b) Use the operational transform given by Eq. 12.23 to
Chapter 12, Problem 12.17(choose chapter or problem)
a) Find the Laplace transform of \(t e^{-a t}\).
b) Use the operational transform given by Eq. 12.23 to find the Laplace transform of \(\frac{d}{d t}\left(t e^{-a t}\right)\).
c) Check your result in part (b) by first differentiating and then transforming the resulting expression.
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