What is inverse oflaplace (200)/((s+10)(s+100)) ?

The answer to inverse oflaplace (200)/((s+10)(s+100)) is 20/9 e^{-10t}-20/9 e^{-100t}

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inverse oflaplace (200)/((s+10)(s+100))

inverse laplace

\frac{200}{( s + 10 ) ( s + 100 )}

\frac{20}{9} e^{- 10 t} - \frac{20}{9} e^{- 100 t}

Solution steps

L^{- 1} {\frac{200}{( s + 10 ) ( s + 100 )}}

Take the partial fraction of

\frac{200}{( s + 10 ) ( s + 100 )} : \frac{20}{9 ( s + 10 )} - \frac{20}{9 ( s + 100 )}

= L^{- 1} {\frac{20}{9 ( s + 10 )} - \frac{20}{9 ( s + 100 )}}

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}{9 ( s + 10 )}} - L^{- 1} {\frac{20}{9 ( s + 100 )}}

L^{- 1} {\frac{20}{9 ( s + 10 )}} : \frac{20}{9} e^{- 10 t}

L^{- 1} {\frac{20}{9 ( s + 100 )}} : \frac{20}{9} e^{- 100 t}

= \frac{20}{9} e^{- 10 t} - \frac{20}{9} e^{- 100 t}

x^{^{''}} - x = 0

\frac{d}{d x} (x^{3} - 2 x^{2} + x - 20)

\int_{0}^{1} x sin (nπ x) d x

\frac{\partial}{\partial y} (y^{4})

\frac{d}{d x} (sec (x) \cdot x^{5})

What is inverse oflaplace (200)/((s+10)(s+100)) ?
The answer to inverse oflaplace (200)/((s+10)(s+100)) is 20/9 e^{-10t}-20/9 e^{-100t}