What is laplacetransform 4t-e^{-3t} ?

The answer to laplacetransform 4t-e^{-3t} is 4/(s^2)-1/(s+3)

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laplacetransform 4t-e^{-3t}

laplace transform

4 t - e^{- 3 t}

\frac{4}{s ^{2}} - \frac{1}{s + 3}

Solution steps

L {4 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)}

= 4 L {t} - L {e^{- 3 t}}

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

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

= 4 \cdot \frac{1}{s ^{2}} - \frac{1}{s + 3}

Refine

4 \frac{1}{s ^{2}} - \frac{1}{s + 3} : \frac{4}{s ^{2}} - \frac{1}{s + 3}

= \frac{4}{s ^{2}} - \frac{1}{s + 3}

f (x) = 20 (x - 1) e^{- 0.5 x}, at x = 4

f (x) = x^{2} + 6

y^{^{''}} - 7 y^{^{'}} = 2 t

\int \frac{5}{25 x ^{2} - 9} d x

- 2 x^{2} + 8, - x - 6

What is laplacetransform 4t-e^{-3t} ?
The answer to laplacetransform 4t-e^{-3t} is 4/(s^2)-1/(s+3)