Determiner-l-origine-de-laplace-1-F-p-p-p-2-2-

Question Number 143523 by lapache last updated on 15/Jun/21

D e t e r m i n e r l^{'} o r i g i n e d e l a p l a c e

1 - F (p) = \frac{p}{{(p + 2)}^{2}}

Answered by Dwaipayan Shikari last updated on 15/Jun/21

F (p) = 1 - \frac{p}{{(p + 2)}^{2}}

L^{- 1} (F (p)) = L^{- 1} (1 - \frac{p}{{(p + 2)}^{2}})

f (t) = p - L^{- 1} (\frac{1}{p + 2}) + L^{- 1} (\frac{2}{{(p + 2)}^{2}})

= {p t}^{0} - e^{- 2 t} - 2 {t e}^{- 2 t}