What is laplacetransform t*e^{,\at} ?

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

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laplacetransform t*e^{,\at}

laplace transform

t \cdot e^{, at}

e^{, at} \frac{1}{s ^{2}}

Solution steps

L {e^{, at} t}

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}

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

= e^{, at} \frac{1}{s ^{2}}

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