What is inverse oflaplace 2/((s+6)(s-4)) ?

The answer to inverse oflaplace 2/((s+6)(s-4)) is -1/5 e^{-6t}+1/5 e^{4t}

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inverse oflaplace 2/((s+6)(s-4))

inverse laplace

\frac{2}{( s + 6 ) ( s - 4 )}

- \frac{1}{5} e^{- 6 t} + \frac{1}{5} e^{4 t}

Solution steps

L^{- 1} {\frac{2}{( s + 6 ) ( s - 4 )}}

Take the partial fraction of

\frac{2}{( s + 6 ) ( s - 4 )} : - \frac{1}{5 ( s + 6 )} + \frac{1}{5 ( s - 4 )}

= L^{- 1} {- \frac{1}{5 ( s + 6 )} + \frac{1}{5 ( 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}{5 ( s + 6 )}} + L^{- 1} {\frac{1}{5 ( s - 4 )}}

L^{- 1} {\frac{1}{5 ( s + 6 )}} : \frac{1}{5} e^{- 6 t}

L^{- 1} {\frac{1}{5 ( s - 4 )}} : \frac{1}{5} e^{4 t}

= - \frac{1}{5} e^{- 6 t} + \frac{1}{5} e^{4 t}

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

\int \frac{2}{100 - 4 x ^{2}} d x

y^{^{'}} + y = 6 x

f (y) = \frac{1}{y}

\int - π csc (\frac{π x}{8}) cot (\frac{π x}{8}) d x

What is inverse oflaplace 2/((s+6)(s-4)) ?
The answer to inverse oflaplace 2/((s+6)(s-4)) is -1/5 e^{-6t}+1/5 e^{4t}