What is laplacetransform t*cos(2t) ?

The answer to laplacetransform t*cos(2t) is -(-s^2+4)/((s^2+4)^2)

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laplacetransform t*cos(2t)

laplace transform

t \cdot cos (2 t)

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

Solution steps

L {t cos (2 t)}

Use Laplace Transform table:

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

For

t cos (2 t) : f (t) = cos (2 t), k = 1

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

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

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

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

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

\frac{\partial}{\partial y} (y - 1)

\frac{\partial}{\partial x} (4 y \cdot e^{5 x^{2} - 2 y})

\int_{1}^{4} 1 + \frac{1}{x ^{2}} d x

\frac{d}{d t} (- 3 cos^{2} (t) sin (t))

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

What is laplacetransform t*cos(2t) ?
The answer to laplacetransform t*cos(2t) is -(-s^2+4)/((s^2+4)^2)