What is inverse oflaplace 4/(2(s-3)^2-50) ?

The answer to inverse oflaplace 4/(2(s-3)^2-50) is -1/5 e^{-2t}+1/5 e^{8t}

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inverse oflaplace 4/(2(s-3)^2-50)

inverse laplace

\frac{4}{2 ( s - 3 ) ^{2} - 50}

- \frac{1}{5} e^{- 2 t} + \frac{1}{5} e^{8 t}

Solution steps

L^{- 1} {\frac{4}{2 ( s - 3 ) ^{2} - 50}}

Take the partial fraction of

\frac{4}{2 ( s - 3 ) ^{2} - 50} : - \frac{1}{5 ( s + 2 )} + \frac{1}{5 ( s - 8 )}

= L^{- 1} {- \frac{1}{5 ( s + 2 )} + \frac{1}{5 ( s - 8 )}}

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 + 2 )}} + L^{- 1} {\frac{1}{5 ( s - 8 )}}

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

L^{- 1} {\frac{1}{5 ( s - 8 )}} : \frac{1}{5} e^{8 t}

= - \frac{1}{5} e^{- 2 t} + \frac{1}{5} e^{8 t}

f (x) = (x^{3} - 4 x + 1) e^{x}, at x = 0

x^{2} + 2 x + 2, 2 x^{2} + 3 x - 4

\frac{d}{d x} (ln (x^{2} + 7))

x \to \frac{π}{2} lim (sin (x))

\int \frac{6}{x ^{2} + 10 x + 16} d x

What is inverse oflaplace 4/(2(s-3)^2-50) ?
The answer to inverse oflaplace 4/(2(s-3)^2-50) is -1/5 e^{-2t}+1/5 e^{8t}