What is laplacetransform t*sin(2t) ?

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

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laplacetransform t*sin(2t)

laplace transform

t \cdot 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}}

y^{^{''}} - y^{^{'}} + y = 13 sin (t)

x \to 0 lim (\frac{4 x}{sin ( x )})

f (x) = 2 + \frac{7}{x} + \frac{2}{x ^{2}}

1 + tan^{2} (x)

\int (1 - csc (x) cot (x)) d x

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