What is inverse oflaplace 3/(s(s+2)) ?

The answer to inverse oflaplace 3/(s(s+2)) is 3/2 \H(t)-3/2 e^{-2t}

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inverse oflaplace 3/(s(s+2))

inverse laplace

\frac{3}{s ( s + 2 )}

\frac{3}{2} H (t) - \frac{3}{2} e^{- 2 t}

Solution steps

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

Take the partial fraction of

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

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

L^{- 1} {\frac{3}{2 s}} : \frac{3}{2} H (t)

L^{- 1} {\frac{3}{2 ( s + 2 )}} : \frac{3}{2} e^{- 2 t}

= \frac{3}{2} H (t) - \frac{3}{2} e^{- 2 t}

\int \frac{1}{8 x} d x

y^{^{''}} - 5 y^{^{'}} + 6 y = 36 t

x \frac{d}{d x} [ln (y)] = 1

y = x, y = 4 x, y = - x + 2

\int 6 sin (3 x) d x

What is inverse oflaplace 3/(s(s+2)) ?
The answer to inverse oflaplace 3/(s(s+2)) is 3/2 \H(t)-3/2 e^{-2t}