What is laplacetransform sqrt(t) ?

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

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laplacetransform sqrt(t)

laplace transform

t

\frac{π}{2 s ^{\frac{3}{2}}}

Solution steps

L {t}

Use Laplace Transform table:

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

L {t} = \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}}}

y^{^{'}} = x^{2} (1 + y^{2})

42 (7 P + 5)^{5}

y^{^{'}} = \frac{x ( y + 1 )}{y ( x + 2 )}

y^{^{'}} - y = 2 e^{2 t}

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