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

The answer to inverse oflaplace (3s+5)/((s-5)(s+2)) is 20/7 e^{5t}+1/7 e^{-2t}

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

inverse laplace

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

\frac{20}{7} e^{5 t} + \frac{1}{7} e^{- 2 t}

Solution steps

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

Take the partial fraction of

\frac{3 s + 5}{( s - 5 ) ( s + 2 )} : \frac{20}{7 ( s - 5 )} + \frac{1}{7 ( s + 2 )}

= L^{- 1} {\frac{20}{7 ( s - 5 )} + \frac{1}{7 ( 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{20}{7 ( s - 5 )}} + L^{- 1} {\frac{1}{7 ( s + 2 )}}

L^{- 1} {\frac{20}{7 ( s - 5 )}} : \frac{20}{7} e^{5 t}

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

= \frac{20}{7} e^{5 t} + \frac{1}{7} e^{- 2 t}

\frac{\partial}{\partial x} (2 x^{3} y + cos (x^{4}))

\int (u^{6} - 2 u^{5} + \frac{2}{7}) d u

\int x^{2} 15 + x^{3} d x

\frac{d}{d x} (\frac{x ^{2} + 3 x - 4}{x + 2})

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

What is inverse oflaplace (3s+5)/((s-5)(s+2)) ?
The answer to inverse oflaplace (3s+5)/((s-5)(s+2)) is 20/7 e^{5t}+1/7 e^{-2t}