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Differential Equations

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Forward Laplace Transform

DIFFEQ-2JX4G7

Recall the definition $\Gamma(p+1)=\int_0^{\infty}e^{-t}*t^pdt$ and the fact that $\Gamma(1/2)=\sqrt{\pi}$.

The Laplace transform of $1/\sqrt{t}$ is

A

$\cfrac{\sqrt{\pi}}{2s^{3/2}}$

B

$\cfrac{1}{\sqrt{\pi s}}$

C

$\cfrac{\sqrt{\pi}}{\sqrt{s}}$

D

$\cfrac{\sqrt{\pi}}{s}$