What is laplacetransform (t-5)/5 ?

The answer to laplacetransform (t-5)/5 is 1/(5s^2)-1/s

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laplacetransform (t-5)/5

laplace transform

\frac{t - 5}{5}

\frac{1}{5 s ^{2}} - \frac{1}{s}

Solution steps

L {\frac{t - 5}{5}}

Expand

= L {\frac{t}{5} - \frac{5}{5}}

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)}

= \frac{1}{5} L {t} - L {\frac{5}{5}}

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

L {\frac{5}{5}} : \frac{1}{s}

= \frac{1}{5} \cdot \frac{1}{s ^{2}} - \frac{1}{s}

Refine

\frac{1}{5} \frac{1}{s ^{2}} - \frac{1}{s} : \frac{1}{5 s ^{2}} - \frac{1}{s}

= \frac{1}{5 s ^{2}} - \frac{1}{s}

What is laplacetransform (t-5)/5 ?
The answer to laplacetransform (t-5)/5 is 1/(5s^2)-1/s