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

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

Popular >

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

laplace transform

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

\frac{4}{s ( s + 2 )}

Solution steps

L {2 (- e^{- 2 t} + 1)}

Expand

2 (1 - e^{- 2 t}) : 2 - 2 e^{- 2 t}

= L {2 - 2 e^{- 2 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)}

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

L {2} : \frac{2}{s}

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

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

Simplify

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

= \frac{4}{s ( s + 2 )}

lo g_{e} (lo g_{e} (x))

f (x) = x^{4} + 5 x^{2} - x, at x = 1

\frac{d}{d x} (\frac{1 - 4 x}{1 + 4 x})

\int ln (cos (x)) \cdot tan (x) d x

\frac{d}{d x} (\frac{4}{x} - x (x + 1))

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