What is inverse oflaplace (s+7)/((s+2)(s-5)) ?

The answer to inverse oflaplace (s+7)/((s+2)(s-5)) is -5/7 e^{-2t}+12/7 e^{5t}

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inverse oflaplace (s+7)/((s+2)(s-5))

inverse laplace

\frac{s + 7}{( s + 2 ) ( s - 5 )}

- \frac{5}{7} e^{- 2 t} + \frac{12}{7} e^{5 t}

Solution steps

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

Take the partial fraction of

\frac{s + 7}{( s + 2 ) ( s - 5 )} : - \frac{5}{7 ( s + 2 )} + \frac{12}{7 ( s - 5 )}

= L^{- 1} {- \frac{5}{7 ( s + 2 )} + \frac{12}{7 ( s - 5 )}}

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}{7 ( s + 2 )}} + L^{- 1} {\frac{12}{7 ( s - 5 )}}

L^{- 1} {\frac{5}{7 ( s + 2 )}} : \frac{5}{7} e^{- 2 t}

L^{- 1} {\frac{12}{7 ( s - 5 )}} : \frac{12}{7} e^{5 t}

= - \frac{5}{7} e^{- 2 t} + \frac{12}{7} e^{5 t}

y = \frac{e ^{x}}{ln ( x )}

f (x) = (8 x^{3} + 2 x^{2})^{4}

\frac{d}{d x} ((1 + 9 x^{2}) (x - x^{2}))

\frac{d}{d x} (arctan (arcsin (x)))

\int 3 y^{5} y^{3} + 1 d y

What is inverse oflaplace (s+7)/((s+2)(s-5)) ?
The answer to inverse oflaplace (s+7)/((s+2)(s-5)) is -5/7 e^{-2t}+12/7 e^{5t}