What is laplacetransform f(t)=t^2e^{,\at} ?

The answer to laplacetransform f(t)=t^2e^{,\at} is e^{,\at} 2/(s^3)

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laplacetransform f(t)=t^2e^{,\at}

laplace transform

f (t) = t^{2} e^{, at}

e^{, at} \frac{2}{s ^{3}}

Solution steps

L {e^{, at} t^{2}}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{, at} L {t^{2}}

L {t^{2}} : \frac{2}{s ^{3}}

= e^{, at} \frac{2}{s ^{3}}

y^{^{'}} + y x^{3} = 4 x^{3}

x \to 0 lim (x^{2} + 9 - 3)

n = 0 \sum \infty 4 (\frac{2}{5})^{n}

f (x) = x x, at x = 3

\frac{\partial}{\partial x} (- \frac{1}{4} (y^{2} + x^{2}))

What is laplacetransform f(t)=t^2e^{,\at} ?
The answer to laplacetransform f(t)=t^2e^{,\at} is e^{,\at} 2/(s^3)