Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: 1 s+o(e-as-e-bs) where a, b, and o are constants. F(s) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function:
1
s+o
F(s) =
-as
- e-bs)
where a, b, and o are constants.
Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] =
e-saF (s), which implies that
f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)
Transcribed Image Text:Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function: 1 s+o F(s) = -as - e-bs) where a, b, and o are constants. Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] = e-saF (s), which implies that f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)
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