What is laplacetransform tsin(9t) ?

The answer to laplacetransform tsin(9t) is (18s)/((s^2+81)^2)

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laplacetransform tsin(9t)

laplace transform

t sin (9 t)

\frac{18 s}{( s ^{2} + 81 ) ^{2}}

Solution steps

L {t sin (9 t)}

Use Laplace Transform table:

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

For

t sin (9 t) : f (t) = sin (9 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {sin (9 t)})

L {sin (9 t)} : \frac{9}{s ^{2} + 81}

\frac{d}{d s} (\frac{9}{s ^{2} + 81}) = - \frac{18 s}{( s ^{2} + 81 ) ^{2}}

= (- 1)^{1} (- \frac{18 s}{( s ^{2} + 81 ) ^{2}})

= \frac{18 s}{( s ^{2} + 81 ) ^{2}}

y = x^{2} - x, y = 0

\frac{2 s + 9}{s ^{2} + 4 s + 40}

\frac{\partial}{\partial t} (\frac{t}{c ^{2} t ^{2} - x ^{2}})

y^{^{''}} + 12 y^{^{'}} + 36 = 0

\frac{\partial}{\partial x} (y e^{x} + x ln (z))

What is laplacetransform tsin(9t) ?
The answer to laplacetransform tsin(9t) is (18s)/((s^2+81)^2)