Question

a) Find the Laplace transform of f(t) = 3t e^{2t} + e^t sin (3t) b) If G(s) = 2/s^2 + (1 + e^{-2s}) / (s^2 + 4) , find L^{-1}{G(s)}

          a) Find the Laplace transform of
f(t) = 3t e^{2t} + e^t sin (3t)
b) If G(s) = 2/s^2 + (1 + e^{-2s}) / (s^2 + 4) , find L^{-1}{G(s)}

Added by Magdalena C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/21/2023

Step 1

For the first term, 3t e^{2t}, we have: $$ \mathcal{L}\{3t e^{2t}\} = \int_0^\infty 3t e^{2t} e^{-st} dt $$ Let's substitute u = s - 2, then s = u + 2: $$ \mathcal{L}\{3t e^{2t}\} = \int_0^\infty 3t e^{-(u+2)t} e^{2t} dt = \int_0^\infty 3t e^{-ut} dt $$ Now, Show more…

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