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

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

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laplacetransform 3t-e^{-3t}

laplace transform

3 t - e^{- 3 t}

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

Solution steps

L {3 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)}

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

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

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

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

Refine

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

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

\frac{\partial}{\partial x} (cos (8 y - 2 x))

\frac{\partial}{\partial y} (\frac{x}{x ^{2} + y ^{2}})

\int 9 x e^{- x} d x

\int_{0}^{1} x^{3} - 3 x^{2} + 2 x d x

y = x^{2} - 5 x + 5

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