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

The answer to inverse oflaplace (2s-3)/(s^2-4) is 7/4 e^{-2t}+1/4 e^{2t}

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

inverse laplace

\frac{2 s - 3}{s ^{2} - 4}

\frac{7}{4} e^{- 2 t} + \frac{1}{4} e^{2 t}

Solution steps

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

Take the partial fraction of

\frac{2 s - 3}{s ^{2} - 4} : \frac{7}{4 ( s + 2 )} + \frac{1}{4 ( s - 2 )}

= L^{- 1} {\frac{7}{4 ( s + 2 )} + \frac{1}{4 ( s - 2 )}}

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{7}{4 ( s + 2 )}} + L^{- 1} {\frac{1}{4 ( s - 2 )}}

L^{- 1} {\frac{7}{4 ( s + 2 )}} : \frac{7}{4} e^{- 2 t}

L^{- 1} {\frac{1}{4 ( s - 2 )}} : \frac{1}{4} e^{2 t}

= \frac{7}{4} e^{- 2 t} + \frac{1}{4} e^{2 t}

\frac{\partial}{\partial x} (ln (8 x^{2} + 7 y^{2} + 3))

\frac{d}{d x} (12 - 3 x - 4 y)

\int \frac{14}{( 49 x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial x} (ln (\frac{x}{y}) + \frac{z - x}{x})

f (x) = 2 x^{2} - 9 x + 10

What is inverse oflaplace (2s-3)/(s^2-4) ?
The answer to inverse oflaplace (2s-3)/(s^2-4) is 7/4 e^{-2t}+1/4 e^{2t}