What is inverse oflaplace (2s)/((s+2)) ?

The answer to inverse oflaplace (2s)/((s+2)) is 2\delta(t)-4e^{-2t}

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inverse oflaplace (2s)/((s+2))

inverse laplace

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

2 δ (t) - 4 e^{- 2 t}

Solution steps

L^{- 1} {\frac{2 s}{( s + 2 )}}

Take the partial fraction of

\frac{2 s}{s + 2} : 2 - \frac{4}{s + 2}

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

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

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

L^{- 1} {2} : 2 δ (t)

L^{- 1} {\frac{4}{s + 2}} : 4 e^{- 2 t}

= 2 δ (t) - 4 e^{- 2 t}

x \to 0 lim (\frac{2 x + 1}{x ^{2}})

f (x) = 8 + 4 x^{2} - 2 x^{3}, at x = 1

\int \frac{e ^{x}}{e ^{x} - 2 e ^{- x}} d x

\frac{x ^{2}}{( x ^{2} + 5 ) ^{3}}

y^{^{'}} = \frac{7 x}{y}

What is inverse oflaplace (2s)/((s+2)) ?
The answer to inverse oflaplace (2s)/((s+2)) is 2\delta(t)-4e^{-2t}