s-1-2-s-2-find-the-inverse-laplace-transformtion-

Question Number 129018 by BHOOPENDRA last updated on 12/Jan/21

\frac{{(\sqrt{s} - 1)}^{2}}{s^{2}} f i n d t h e i n v e r s e l a p l a c e t r a n s f o r m t i o n

Answered by Dwaipayan Shikari last updated on 12/Jan/21

L^{- 1} (\frac{1}{s} - \frac{2}{s^{\frac{3}{2}}} + \frac{1}{s^{2}})

= 1 - 4 \sqrt{\frac{t}{π}} + t [\int_{0}^{\infty} t^{\frac{1}{2}} e^{- s t} d t = \frac{\sqrt{π}}{2 s^{\frac{3}{2}}} \Rightarrow \frac{2}{\sqrt{π}} L (\sqrt{t}) = \frac{1}{\sqrt{s^{3}}}]

Commented by BHOOPENDRA last updated on 12/Jan/21

a n s . i s n o t c r c t s i r \dots i t s i n t f o r m

Commented by Dwaipayan Shikari last updated on 12/Jan/21

I t i s a l r e a d y i n^{'} t^{'} f o r m

t + 1 - \frac{4 \sqrt{t}}{\sqrt{π}}

Commented by BHOOPENDRA last updated on 12/Jan/21

t h e A n s i s

\frac{t^{\frac{- 2}{3}} + 3 t^{\frac{1}{3}}}{⌈ \frac{1}{3}} s o c a n y o u p l z e x p l a i n t h i s

Commented by Dwaipayan Shikari last updated on 12/Jan/21

M a y b e e r r o r i n q u e s t i o n