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}

\frac{d}{d x} (e^{x^{2} - 5 x})

\int_{0}^{9} π (2 y)^{2} d y

\frac{d y}{d x} + 4 y - e^{- x} = 0

\frac{e ^{- s}}{s ^{2} + 2 s + 2}

0

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