What is laplacetransform t^2e^{4t} ?

The answer to laplacetransform t^2e^{4t} is 2/((s-4)^3)

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laplacetransform t^2e^{4t}

laplace transform

t^{2} e^{4 t}

\frac{2}{( s - 4 ) ^{3}}

Solution steps

L {e^{4 t} t^{2}}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t^{2} e^{4 t} : f (t) = e^{4 t}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{4 t}})

L {e^{4 t}} : \frac{1}{s - 4}

\frac{d ^{2}}{d s ^{2}} (\frac{1}{s - 4}) = \frac{2}{( s - 4 ) ^{3}}

= (- 1)^{2} \frac{2}{( s - 4 ) ^{3}}

= \frac{2}{( s - 4 ) ^{3}}

\frac{\partial}{\partial y} (x^{2} ln (y))

(1 + x^{16}) y^{^{'}} + 16 x^{15} y = 9 x^{13}

\frac{d}{d x} (e^{x} cos (2 x) + e^{x} sin (2 x))

\frac{d}{d x} (\frac{x + 2}{x + 1})

\int x^{2} e^{x^{2}} d x

What is laplacetransform t^2e^{4t} ?
The answer to laplacetransform t^2e^{4t} is 2/((s-4)^3)