What is laplacetransform (e^{2t}-e^1)/2 ?

The answer to laplacetransform (e^{2t}-e^1)/2 is 1/(2(s-2))-e/(2s)

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laplacetransform (e^{2t}-e^1)/2

laplace transform

\frac{e ^{2 t} - e ^{1}}{2}

\frac{1}{2 ( s - 2 )} - \frac{e}{2 s}

Solution steps

L {\frac{e ^{2 t} - e ^{1}}{2}}

Expand

= L {\frac{e ^{2 t}}{2} - \frac{e ^{1}}{2}}

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}{2} L {e^{2 t}} - L {\frac{e ^{1}}{2}}

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

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

= \frac{1}{2} \cdot \frac{1}{s - 2} - \frac{e}{2 s}

Refine

\frac{1}{2} \frac{1}{s - 2} - \frac{e}{2 s} : \frac{1}{2 ( s - 2 )} - \frac{e}{2 s}

= \frac{1}{2 ( s - 2 )} - \frac{e}{2 s}

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