What is inverse oflaplace (s+5)/((s+2)(s+3)) ?

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

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inverse oflaplace (s+5)/((s+2)(s+3))

inverse laplace

\frac{s + 5}{( s + 2 ) ( s + 3 )}

3 e^{- 2 t} - 2 e^{- 3 t}

Solution steps

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

Take the partial fraction of

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

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

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

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

= 3 e^{- 2 t} - 2 e^{- 3 t}

x \to \infty lim (\frac{8}{x} - 8)

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

cos (2 x + π)

5 t y^{^{'}} + (10 + 5 t (\frac{2 ( t - 7 )}{7 t})) y = 0

\frac{\partial}{\partial x} (10 sin (x y))

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