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

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

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

inverse laplace

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

2 e^{- t} - e^{- 2 t}

Solution steps

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

Take the partial fraction of

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

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

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

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

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

y^{2} - 2 x = 2, x - y = 3

\int \frac{2}{x - 1} d x

\int \frac{4 x + 6}{x ^{2} + 3 x + 1} d x

y = \frac{( 2 x ^{2} + 7 )}{x ^{2} + 3}

x \to 3 π + lim (csc (x))

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