The Laplace transform of t^(-3/2) e^(-1/t) is denoted F(s). Show that (dF)/(ds)=-(F)/(s^(1/2))

Valery Cook

Valery Cook

Answered question

2022-10-18

The Laplace transform of t 3 / 2 e 1 / t is denoted F(s). Show that
d F d s = F s 1 / 2
not sure how to get this.
I tried differentiating F ( s ) = 0 t 3 / 2 e 1 / t e s t d t
d F d s = 0 t 1 / 2 e 1 / t e s t d t

Answer & Explanation

Layne Murillo

Layne Murillo

Beginner2022-10-19Added 14 answers

Let u s t = 1 or s t = 1 u then
d F d s = 0 t 1 / 2 e 1 / t e s t d t = 1 s 0 u 3 / 2 e 1 / u e s u   d u = 1 s F

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