What is laplacetransform t*e^{2t} ?

The answer to laplacetransform t*e^{2t} is 1/((s-2)^2)

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laplacetransform t*e^{2t}

laplace transform

t \cdot e^{2 t}

\frac{1}{( s - 2 ) ^{2}}

Solution steps

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

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

L {e^{2 t}} : \frac{1}{s - 2}

\frac{d}{d s} (\frac{1}{s - 2}) = - \frac{1}{( s - 2 ) ^{2}}

= (- 1)^{1} (- \frac{1}{( s - 2 ) ^{2}})

= \frac{1}{( s - 2 ) ^{2}}

\frac{d y}{d t} + \frac{1}{2} y = \frac{1}{2} e^{\frac{t}{3}}

n = 0 \sum \infty 5 (- \frac{10}{11})^{n}

x \to 0 - lim (arctan (x))

\int (3 x^{2} + 1)^{6} d x

f (x) = (\frac{x ^{2}}{8 - 6 x})

What is laplacetransform t*e^{2t} ?
The answer to laplacetransform t*e^{2t} is 1/((s-2)^2)