What is inverse oflaplace ((35+16))/(s^2-s-6) ?

The answer to inverse oflaplace ((35+16))/(s^2-s-6) is -51/5 e^{-2t}+51/5 e^{3t}

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inverse oflaplace ((35+16))/(s^2-s-6)

inverse laplace

\frac{( 35 + 16 )}{s ^{2} - s - 6}

- \frac{51}{5} e^{- 2 t} + \frac{51}{5} e^{3 t}

Solution steps

L^{- 1} {\frac{( 35 + 16 )}{s ^{2} - s - 6}}

Take the partial fraction of

\frac{35 + 16}{s ^{2} - s - 6} : - \frac{51}{5 ( s + 2 )} + \frac{51}{5 ( s - 3 )}

= L^{- 1} {- \frac{51}{5 ( s + 2 )} + \frac{51}{5 ( 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{51}{5 ( s + 2 )}} + L^{- 1} {\frac{51}{5 ( s - 3 )}}

L^{- 1} {\frac{51}{5 ( s + 2 )}} : \frac{51}{5} e^{- 2 t}

L^{- 1} {\frac{51}{5 ( s - 3 )}} : \frac{51}{5} e^{3 t}

= - \frac{51}{5} e^{- 2 t} + \frac{51}{5} e^{3 t}

\int \frac{5}{x ^{2} + 9} d x

\int \frac{x}{sin ( x ^{2} )} d x

y = x^{2} - 2 x + 1, (- 1, 4)

\frac{\partial}{\partial x} (5^{8^{x^{2}}})

\int (e^{x} + 1) \cdot (x - 4) d x

What is inverse oflaplace ((35+16))/(s^2-s-6) ?
The answer to inverse oflaplace ((35+16))/(s^2-s-6) is -51/5 e^{-2t}+51/5 e^{3t}