What is laplacetransform t^2e^{5t} ?

The answer to laplacetransform t^2e^{5t} is 2/((s-5)^3)

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laplacetransform t^2e^{5t}

laplace transform

t^{2} e^{5 t}

\frac{2}{( s - 5 ) ^{3}}

Solution steps

L {e^{5 t} t^{2}}

Use Laplace Transform table:

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

For

t^{2} e^{5 t} : f (t) = e^{5 t}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{5 t}})

L {e^{5 t}} : \frac{1}{s - 5}

\frac{d ^{2}}{d s ^{2}} (\frac{1}{s - 5}) = \frac{2}{( s - 5 ) ^{3}}

= (- 1)^{2} \frac{2}{( s - 5 ) ^{3}}

= \frac{2}{( s - 5 ) ^{3}}

y = x, y = x^{3}

n = 0 \sum \infty n (\frac{1}{3})^{n}

x \to 0 lim (cos (\frac{4}{x}))

(- \frac{3}{4}, \frac{1}{4}), (\frac{1}{2}, - \frac{3}{2})

What is laplacetransform t^2e^{5t} ?
The answer to laplacetransform t^2e^{5t} is 2/((s-5)^3)