Question

Use the Differential of Transforms Theorem (Theorem 2 in section 7.4) to find the inverse Laplace...

Use the Differential of Transforms Theorem (Theorem 2 in section 7.4) to find the inverse Laplace transform of F(s) = ln((s+2)/(s-2)) + ln((s+3)/(s-3)).

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Answer #1

According to the differential of transform theorem,

L {-t.f(t)} = F'(s)

So, L​​​​​​-1​​​​ {F'(s)} = -t.f(t)

Therefore the inverse Laplace transform of F(s) is equal to

f(t) = (e​​​​​​-2t​​​ +e​​​-3t -e​2t -e​3t )/t

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