What is laplacetransform 2t-e^{-3t} ?

The answer to laplacetransform 2t-e^{-3t} is 2/(s^2)-1/(s+3)

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laplacetransform 2t-e^{-3t}

laplace transform

2 t - e^{- 3 t}

\frac{2}{s ^{2}} - \frac{1}{s + 3}

Solution steps

L {2 t - e^{- 3 t}}

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)}

= 2 L {t} - L {e^{- 3 t}}

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

L {e^{- 3 t}} : \frac{1}{s + 3}

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

Refine

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

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

What is laplacetransform 2t-e^{-3t} ?
The answer to laplacetransform 2t-e^{-3t} is 2/(s^2)-1/(s+3)