What is laplacetransform 3tcos(3t) ?

The answer to laplacetransform 3tcos(3t) is -(3(-s^2+9))/((s^2+9)^2)

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laplacetransform 3tcos(3t)

laplace transform

3 t cos (3 t)

- \frac{3 ( - s ^{2} + 9 )}{( s ^{2} + 9 ) ^{2}}

Solution steps

L {3 t cos (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 cos (3 t)}

L {t cos (3 t)} : - \frac{- s ^{2} + 9}{( s ^{2} + 9 ) ^{2}}

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

Refine

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

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

x \to 1 lim (e^{x - 2})

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

y^{^{''}} + 16 y = 4 sec (4 t)

\frac{d}{d x} (ln (2 x^{4} - x^{3} + 3 x^{2} - 3 x))

f (x) = ln (1)

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