Ta. Determine the Laplace Transform of eachfunctiona) +?et_3+e+Be-4t-

Answered: Ta. Determine the Laplace Transform of…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.4: Definition Of Function

Problem 17E

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Ta. Determine the Laplace Transform of each
function
a) +?et_3+e+Be
-4t
-

Expert Solution

Step 1

Consider the given equation.

$t^{2} e^{- 4 t} - 3 t e^{- 4 t} + 8 e^{- 4 t}$

Apply the Laplace transformation.

$\begin{array}{rcl} L \{t^{2} e^{- 4 t} - 3 t e^{- 4 t} + 8 e^{- 4 t}\} & = & L \{t^{2} e^{- 4 t}\} - 3 L \{t e^{- 4 t}\} + 8 L \{e^{- 4 t}\} \\ = & \frac{2!}{s^{2 + 1}} (\frac{1}{s + 4}) - 3 (\frac{1}{s^{1 + 1}}) (\frac{1}{s + 4}) + 8 (\frac{1}{s + 4}) \\ = & \frac{1}{s + 4} [\frac{2}{s^{3}} - \frac{3}{s^{2}} + 8] \end{array}$

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