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

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

Popular >

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

inverse laplace

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

6 e^{- 2 t} - 6 e^{- 3 t}

Solution steps

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

Take the partial fraction of

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

= L^{- 1} {\frac{6}{s + 2} - \frac{6}{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{6}{s + 2}} - L^{- 1} {\frac{6}{s + 3}}

L^{- 1} {\frac{6}{s + 2}} : 6 e^{- 2 t}

L^{- 1} {\frac{6}{s + 3}} : 6 e^{- 3 t}

= 6 e^{- 2 t} - 6 e^{- 3 t}

x \to 4 lim (\frac{x ^{2} + x}{x + 1})

y = 17 - x^{2}, x = 0, y = 0

\int \frac{( x ^{2} - 1 )}{( x ^{2} + 1 )} d x

\frac{\partial}{\partial x} (2 x e^{y})

\frac{1}{x}, at x = 3

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