What is inverse oflaplace ((s+1))/((s+2)(s-3)) ?

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

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inverse oflaplace ((s+1))/((s+2)(s-3))

inverse laplace

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

\frac{1}{5} e^{- 2 t} + \frac{4}{5} e^{3 t}

Solution steps

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

Take the partial fraction of

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

= L^{- 1} {\frac{1}{5 ( s + 2 )} + \frac{4}{5 ( 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}{5 ( s + 2 )}} + L^{- 1} {\frac{4}{5 ( s - 3 )}}

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

L^{- 1} {\frac{4}{5 ( s - 3 )}} : \frac{4}{5} e^{3 t}

= \frac{1}{5} e^{- 2 t} + \frac{4}{5} e^{3 t}

4 y - y^{^{''}} = 10 e^{- 3 x}

\int ln (x) + 1 d x

\int 2 sin (x) + cos (x) d x

\int_{- 1}^{2} (x^{2} + 1) d x

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

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