What is inverse oflaplace {s/(s^2+2s-3)} ?

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

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inverse oflaplace {s/(s^2+2s-3)}

inverse laplace

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

\frac{1}{4} e^{t} + \frac{3}{4} e^{- 3 t}

Solution steps

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

Take the partial fraction of

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

= L^{- 1} {\frac{1}{4 ( s - 1 )} + \frac{3}{4 ( 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{1}{4 ( s - 1 )}} + L^{- 1} {\frac{3}{4 ( s + 3 )}}

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

L^{- 1} {\frac{3}{4 ( s + 3 )}} : \frac{3}{4} e^{- 3 t}

= \frac{1}{4} e^{t} + \frac{3}{4} e^{- 3 t}

\int ln (s) ec x tan (x) d x

10 x^{3} - 30 x + 120

\frac{d}{d x} (2 x^{2} y^{2})

z + 3 (\frac{1}{z ^{2}})

\frac{d y}{d x} + y tan (x) = 2 x cos (x)

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