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

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

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

inverse laplace

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

\frac{5}{3} e^{2 t} - \frac{2}{3} e^{- t}

Solution steps

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

Take the partial fraction of

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

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

L^{- 1} {\frac{5}{3 ( s - 2 )}} : \frac{5}{3} e^{2 t}

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

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

x \to 1 lim (2 - x^{2})

\frac{d x}{d y} - sin (x + y) = 0

5^{6 x}

y = 15 x ln (13 x)

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

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