What is laplacetransform (-4/3)*e^{-2t}+(-2/3)*e^t ?

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

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laplacetransform (-4/3)e^{-2t}+(-2/3)e^t

laplace transform

(- \frac{4}{3}) \cdot e^{- 2 t} + (- \frac{2}{3}) \cdot e^{t}

- \frac{4}{3 ( s + 2 )} - \frac{2}{3 ( s - 1 )}

Solution steps

L {(- \frac{4}{3}) e^{- 2 t} + (- \frac{2}{3}) e^{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)}

= (- \frac{4}{3}) L {e^{- 2 t}} + (- \frac{2}{3}) L {e^{t}}

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

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

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

Refine

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

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

l a pl a ce t r an s f or m cos (t + 1)

\int \frac{x ^{2} + x}{x ^{2} + x + 1} d x

d er i v a t i v e y = e^{- 11 x}

n = 1 \sum \infty n^{3}

\frac{d x}{d t} = 3 t^{2}

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