ln[(s-1)/(s+1)] Laplace inverse的詳細過程?

2016-06-06 4:29 pm

回答 (1)

2016-06-07 7:44 am
✔ 最佳答案
令 F(s) = ln [ (s-1) / (s+1) ] = ln (s-1) - ln (s+1)
dF/ds = 1/(s-1) - 1/(s+1)
ℒ⁻¹ { dF/ds } = ℒ⁻¹ { 1/(s-1) } - ℒ⁻¹ { 1/(s+1) }
- t * f(t) = e^t - e^(-t)
f(t) = [ e^t - e^(-t) ] / ( - t ) = [ e^(-t) - e^t ] / t

Ans: [ e^(-t) - e^t ] / t


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