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

The answer to inverse oflaplace (s+3)/(s(s+2)) is 3/2 \H(t)-1/2 e^{-2t}

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

inverse laplace

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

\frac{3}{2} H (t) - \frac{1}{2} e^{- 2 t}

Solution steps

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

Take the partial fraction of

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

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

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

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

= \frac{3}{2} H (t) - \frac{1}{2} e^{- 2 t}

x \to 2 lim (\frac{2 x - 4}{3 - 2 x})

\frac{d}{d x} (ln tan (\frac{x}{2}) + C)

\frac{d ^{2}}{d x ^{2}} (3 sec (x))

\int 3 cos (x) d x

\frac{d}{d x} (x^{2} + k)

What is inverse oflaplace (s+3)/(s(s+2)) ?
The answer to inverse oflaplace (s+3)/(s(s+2)) is 3/2 \H(t)-1/2 e^{-2t}