To find: The Laplace transform of L[e^{-3t}t^4]

Suman Cole 2020-12-28 Answered
To find:
The Laplace transform of L[e3tt4]
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Expert Answer

joshyoung05M
Answered 2020-12-29 Author has 97 answers
Step 1
To find:
Laplace transform of L[e3tt4]
Step 2
Use the Laplace transform:L{tkf(t)}=(1)kdkdsk(L{f(t)})
Here k=4 and f(t)=e3t
L{t4e3t}=(1)4d4ds4(L{e3t})
=d4ds4(L{e3t})
Use the Laplace transform: L{eat}=1s+a
L{t4e3t}=d4ds4(L{e3t})
=d4ds4(1s+3)
=d3ds3dds1s+3
=d3ds3(1(s+3)2)
=d2ds2dds(1(s+3)2)
=d2ds2(12(s+3)3)
=ddsdds((12)/(s+3)3)
=dds(123(s+3)4)
=(1234(s+3)5)
=(4!)(s+3)5
Hence the Laplace transform L[e3tt4]=(4!)(s+3)5
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