What is laplacetransform t^2*e^{3t} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

laplacetransform t^2*e^{3t}

laplace transform

t^{2} \cdot e^{3 t}

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

Solution steps

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

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

L {e^{3 t}} : \frac{1}{s - 3}

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

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

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

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