What is laplacetransform 4t*sin(3t) ?

The answer to laplacetransform 4t*sin(3t) is (24s)/((s^2+9)^2)

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laplacetransform 4t*sin(3t)

laplace transform

4 t \cdot sin (3 t)

\frac{24 s}{( s ^{2} + 9 ) ^{2}}

Solution steps

L {4 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)}

= 4 L {t sin (3 t)}

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

= 4 \cdot \frac{6 s}{( s ^{2} + 9 ) ^{2}}

Refine

4 \frac{6 s}{( s ^{2} + 9 ) ^{2}} : \frac{24 s}{( s ^{2} + 9 ) ^{2}}

= \frac{24 s}{( s ^{2} + 9 ) ^{2}}

\frac{x y ^{^{'}}}{y ^{2}} sin (\frac{x}{y}) = \frac{1}{y} sin (\frac{x}{y})

\frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

\int 13 cos^{3} (x) d x

\frac{d P}{d t} = \frac{P}{5} - \frac{P ^{2}}{75}, P (0) = 5

y = - sin (x)

What is laplacetransform 4t*sin(3t) ?
The answer to laplacetransform 4t*sin(3t) is (24s)/((s^2+9)^2)