What is inverse oflaplace ((s))/(s^2+5s+6) ?

The answer to inverse oflaplace ((s))/(s^2+5s+6) is -2e^{-2t}+3e^{-3t}

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inverse oflaplace ((s))/(s^2+5s+6)

inverse laplace

\frac{( s )}{s ^{2} + 5 s + 6}

- 2 e^{- 2 t} + 3 e^{- 3 t}

Solution steps

L^{- 1} {\frac{( s )}{s ^{2} + 5 s + 6}}

Take the partial fraction of

\frac{s}{s ^{2} + 5 s + 6} : - \frac{2}{s + 2} + \frac{3}{s + 3}

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

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

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

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

= - 2 e^{- 2 t} + 3 e^{- 3 t}

\frac{d}{d x} (\frac{( - 2 x - 3 ) ^{7}}{( 4 x + 2 ) ^{4}})

\frac{d y}{d x} + 10 y = 8

\int_{1}^{5} x^{3} - 5 x^{2} - x + 5 d x

\frac{d}{d y} (2 1 - y^{2} - (\frac{x}{4})^{2})

f (x) = 17.19 8^{2} - x^{2}

What is inverse oflaplace ((s))/(s^2+5s+6) ?
The answer to inverse oflaplace ((s))/(s^2+5s+6) is -2e^{-2t}+3e^{-3t}