What is laplacetransform te^{2t}cos(3t) ?

The answer to laplacetransform te^{2t}cos(3t) is -(-s^2+4s+5)/((s^2-4s+13)^2)

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laplacetransform te^{2t}cos(3t)

laplace transform

t e^{2 t} cos (3 t)

- \frac{- s ^{2} + 4 s + 5}{( s ^{2} - 4 s + 13 ) ^{2}}

Solution steps

L {e^{2 t} t cos (3 t)}

Use Laplace Transform table:

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

For

t e^{2 t} cos (3 t) : f (t) = e^{2 t} cos (3 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{2 t} cos (3 t)})

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

\frac{d}{d s} (\frac{s - 2}{( s - 2 ) ^{2} + 9}) = \frac{- s ^{2} + 4 s + 5}{( s ^{2} - 4 s + 13 ) ^{2}}

= (- 1)^{1} \frac{- s ^{2} + 4 s + 5}{( s ^{2} - 4 s + 13 ) ^{2}}

= - \frac{- s ^{2} + 4 s + 5}{( s ^{2} - 4 s + 13 ) ^{2}}

9 y^{^{'}} - 9 tan (x) y = \frac{20}{cos ( x )}

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

n = 0 \sum \infty \frac{100}{n}

\int x^{- 2} (3 x^{4} + 4 x^{2} - 5) d x

x^{2} + y^{2} = 23

What is laplacetransform te^{2t}cos(3t) ?
The answer to laplacetransform te^{2t}cos(3t) is -(-s^2+4s+5)/((s^2-4s+13)^2)