What is laplacetransform tsin(2t) ?

The answer to laplacetransform tsin(2t) is (4s)/((s^2+4)^2)

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laplacetransform tsin(2t)

laplace transform

t sin (2 t)

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

Solution steps

L {t sin (2 t)}

Use Laplace Transform table:

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

For

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

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

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

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

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

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

\frac{d}{d h} (\frac{n ^{2} h ^{2}}{8 m L ^{2}})

t^{2} y^{^{''}} + 19 t y^{^{'}} + 145 y = 0

\int \frac{x}{x ^{2} + 8} d x

\frac{d}{d x} (x^{8} arctan (x^{3}))

y^{^{'}} = k (y - 70)

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