What is laplacetransform (t-3)^2 ?

The answer to laplacetransform (t-3)^2 is 2/(s^3)-6/(s^2)+9/s

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laplacetransform (t-3)^2

laplace transform

(t - 3)^{2}

\frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s}

Solution steps

L {(t - 3)^{2}}

Expand

(t - 3)^{2} : t^{2} - 6 t + 9

= L {t^{2} - 6 t + 9}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} - 6 L {t} + L {9}

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

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

L {9} : \frac{9}{s}

= \frac{2}{s ^{3}} - 6 \cdot \frac{1}{s ^{2}} + \frac{9}{s}

Refine

\frac{2}{s ^{3}} - 6 \frac{1}{s ^{2}} + \frac{9}{s} : \frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s}

= \frac{2}{s ^{3}} - \frac{6}{s ^{2}} + \frac{9}{s}

What is laplacetransform (t-3)^2 ?
The answer to laplacetransform (t-3)^2 is 2/(s^3)-6/(s^2)+9/s