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

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

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laplacetransform t^2e^{2t}

laplace transform

t^{2} e^{2 t}

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

Solution steps

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

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

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

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

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

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

b \to \infty lim (b c)

\int \frac{1}{5 + 3 x ^{2}} d x

24 x - 4 x

\frac{d y}{d x} = \frac{1}{2} x + 1

f (x) = \frac{1}{x}, g (x) = \frac{1}{3}, [2, 5]

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