What is laplacetransform f(k)ke^{-3k} ?

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

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laplacetransform f(k)ke^{-3k}

laplace transform

f (k) k e^{- 3 k}

\frac{k ^{2} e ^{- 3 k}}{s ^{2}}

Solution steps

L {(k) k e^{- 3 k} f}

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)}

= kk e^{- 3 k} L {f}

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

= kk e^{- 3 k} \frac{1}{s ^{2}}

Refine

kk e^{- 3 k} \frac{1}{s ^{2}} : \frac{k ^{2} e ^{- 3 k}}{s ^{2}}

= \frac{k ^{2} e ^{- 3 k}}{s ^{2}}

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