What is inverse oflaplace (16)/((s-1)(s+1)) ?

The answer to inverse oflaplace (16)/((s-1)(s+1)) is 8e^t-8e^{-t}

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inverse oflaplace (16)/((s-1)(s+1))

inverse laplace

\frac{16}{( s - 1 ) ( s + 1 )}

8 e^{t} - 8 e^{- t}

Solution steps

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

Take the partial fraction of

\frac{16}{( s - 1 ) ( s + 1 )} : \frac{8}{s - 1} - \frac{8}{s + 1}

= L^{- 1} {\frac{8}{s - 1} - \frac{8}{s + 1}}

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{8}{s - 1}} - L^{- 1} {\frac{8}{s + 1}}

L^{- 1} {\frac{8}{s - 1}} : 8 e^{t}

L^{- 1} {\frac{8}{s + 1}} : 8 e^{- t}

= 8 e^{t} - 8 e^{- t}

\frac{2}{s ^{2} ( s ^{2} + 25 )}

\frac{\partial}{\partial x} (4 y sin (2 x))

e^{y} y^{^{'}} = e^{y} + 7 x

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

\frac{d}{d x} (5 x^{7} sin (x))

What is inverse oflaplace (16)/((s-1)(s+1)) ?
The answer to inverse oflaplace (16)/((s-1)(s+1)) is 8e^t-8e^{-t}