What is laplacetransform t^2cos(3t) ?

The answer to laplacetransform t^2cos(3t) is -(2s(-s^2+27))/((s^2+9)^3)

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laplacetransform t^2cos(3t)

laplace transform

t^{2} cos (3 t)

- \frac{2 s ( - s ^{2} + 27 )}{( s ^{2} + 9 ) ^{3}}

Solution steps

L {t^{2} cos (3 t)}

Use Laplace Transform table:

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

For

t^{2} cos (3 t) : f (t) = cos (3 t), k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {cos (3 t)})

L {cos (3 t)} : \frac{s}{s ^{2} + 9}

\frac{d ^{2}}{d s ^{2}} (\frac{s}{s ^{2} + 9}) = - \frac{2 s ( - s ^{2} + 27 )}{( s ^{2} + 9 ) ^{3}}

= (- 1)^{2} (- \frac{2 s ( - s ^{2} + 27 )}{( s ^{2} + 9 ) ^{3}})

= - \frac{2 s ( - s ^{2} + 27 )}{( s ^{2} + 9 ) ^{3}}

x \to 13 lim (x^{4} - 10 x^{2} - 20)

x \to \infty lim (x e^{(\frac{1}{x})})

\frac{\partial}{\partial x} (e^{x} cos (2 x))

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

5 x - 8 y x^{2} + 1 \frac{d y}{d x} = 0

What is laplacetransform t^2cos(3t) ?
The answer to laplacetransform t^2cos(3t) is -(2s(-s^2+27))/((s^2+9)^3)