Answer
See below
Work Step by Step
Using the Convolution Theorem
$L^{-1}[F(s)* G(s)]=L^{-1}[\frac{2}{s^2+6s+10}.\frac{2}{s-4}]\\
=L^{-1}[\frac{2}{s^2+6s+10}].L^{-1}[\frac{2}{s-4}]\\
=2e^{4t}*2e^{-3t} \sin t\\
=\int^t_0 e^{4t-7x}\sin (x)dx$
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 - 10.9 The Convolution Integral - Problems - Page 716: 23
Update this answer!
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
