What is laplacetransform x^{1/2} ?

The answer to laplacetransform x^{1/2} is (sqrt(pi))/(2s^{3/2)}

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laplacetransform x^{1/2}

laplace transform

x^{\frac{1}{2}}

\frac{π}{2 s ^{\frac{3}{2}}}

Solution steps

L {x^{\frac{1}{2}}}

Use Laplace Transform table:

L {t^{n - 1/2}} = \frac{( 2 n - 1 ) !! π}{2 ^{n} s ^{n + 1/2}}

L {x^{\frac{1}{2}}} = \frac{1 \cdot π}{2 ^{1} s ^{\frac{3}{2}}}

= \frac{1 \cdot π}{2 ^{1} s ^{\frac{3}{2}}}

= \frac{π}{2 s ^{\frac{3}{2}}}

\frac{3 x d x}{x ^{2} + 2} = - \frac{y d y}{y ^{2} + 1}

\frac{d}{d x} (\frac{4 x}{x ^{2} + 3})

\frac{d y}{d x} = \frac{cos ( 7 x )}{e ^{7 y}}

\int cos (x) sin (x) - x y^{2} d x

\frac{d x}{d t} = (3 x t^{2})

What is laplacetransform x^{1/2} ?
The answer to laplacetransform x^{1/2} is (sqrt(pi))/(2s^{3/2)}