What is laplacetransform 3tsin(3t) ?

The answer to laplacetransform 3tsin(3t) is (18s)/((s^2+9)^2)

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laplacetransform 3tsin(3t)

laplace transform

3 t sin (3 t)

\frac{18 s}{( s ^{2} + 9 ) ^{2}}

Solution steps

L {3 t sin (3 t)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 3 L {t sin (3 t)}

L {t sin (3 t)} : \frac{6 s}{( s ^{2} + 9 ) ^{2}}

= 3 \cdot \frac{6 s}{( s ^{2} + 9 ) ^{2}}

Refine

3 \frac{6 s}{( s ^{2} + 9 ) ^{2}} : \frac{18 s}{( s ^{2} + 9 ) ^{2}}

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

\frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x} = 0

y^{^{'}} = (x - 4) e^{- 2 y}, y (4) = ln (4)

\frac{d}{d x} (2 x^{- \frac{14}{5}})

x \to 3 lim (\frac{6 x}{x ^{2} - 9})

\int - t^{2} d t

What is laplacetransform 3tsin(3t) ?
The answer to laplacetransform 3tsin(3t) is (18s)/((s^2+9)^2)