What is inverse oflaplace 3/(s^3) ?

The answer to inverse oflaplace 3/(s^3) is (3t^2)/2

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inverse oflaplace 3/(s^3)

inverse laplace

\frac{3}{s ^{3}}

\frac{3 t ^{2}}{2}

Solution steps

L^{- 1} {\frac{3}{s ^{3}}}

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

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{3}{2} L^{- 1} {\frac{2}{s ^{3}}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{2}{s ^{3}}} = t^{2}

= \frac{3}{2} t^{2}

= \frac{3 t ^{2}}{2}

y^{^{'}} + 10 x^{4} y = 50 x^{9} e^{3 x^{5}}

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x \to - 1 lim (\frac{4}{x ^{2} + 2 x + 3})

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What is inverse oflaplace 3/(s^3) ?
The answer to inverse oflaplace 3/(s^3) is (3t^2)/2