Question

Determine the Laplace transform.

Answer 1

\[\frac{ e ^{-2s}-3e ^{-4s} }{ s+2 }\]

Answer 2

I meant inverse Laplace

Answer 3

\[\mathcal L^{-1}\left\{\frac{ e ^{-2s}-3e ^{-4s} }{ s+2 }\right\}\]

Answer 4

\[=\mathcal L^{-1}\left\{\frac{ e ^{-2s} }{ s+2 }\right\}-\mathcal L^{-1}\left\{\frac{3e ^{-4s} }{ s+2 }\right\}\]

Answer 5

\[=\mathcal L^{-1}\left\{\frac{ e ^{-2s} }{ s+2 }\right\}-3\mathcal L^{-1}\left\{\frac{e ^{-4s} }{ s+2 }\right\}\]

Answer 6

now use

\[\mathcal L\big\{f(t-a)h(t-a)\big\}=e^{as}F(s)\]