What is inverse oflaplace ((s+2))/(s^2+7s+12) ?

The answer to inverse oflaplace ((s+2))/(s^2+7s+12) is -e^{-3t}+2e^{-4t}

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inverse oflaplace ((s+2))/(s^2+7s+12)

inverselaplace

- e^{- 3 t} + 2 e^{- 4 t}

Solution steps

L^{- 1} {\frac{( s + 2 )}{s ^{2} + 7 s + 12}}

Take the partial fraction of

\frac{s + 2}{s ^{2} + 7 s + 12} : - \frac{1}{s + 3} + \frac{2}{s + 4}

= L^{- 1} {- \frac{1}{s + 3} + \frac{2}{s + 4}}

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{1}{s + 3}} + L^{- 1} {\frac{2}{s + 4}}

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

L^{- 1} {\frac{2}{s + 4}} : 2 e^{- 4 t}

= - e^{- 3 t} + 2 e^{- 4 t}

What is inverse oflaplace ((s+2))/(s^2+7s+12) ?
The answer to inverse oflaplace ((s+2))/(s^2+7s+12) is -e^{-3t}+2e^{-4t}