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

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

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inverse oflaplace s/((s+2))

inverse laplace

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

δ (t) - 2 e^{- 2 t}

Solution steps

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

Take the partial fraction of

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

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

L^{- 1} {1} : δ (t)

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

= δ (t) - 2 e^{- 2 t}

y^{^{'}} = \frac{y}{x}, y (2) = 2

\frac{d}{d x} (e^{- ∣ x ∣})

x \to - 2 lim (\frac{x + 2}{2 x + 4})

\int \frac{1}{( x ^{2} - 1 ) ^{\frac{3}{2}}} d x

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