What is inverse oflaplace {(10)/(s(s+2))} ?

The answer to inverse oflaplace {(10)/(s(s+2))} is 5\H(t)-5e^{-2t}

Popular >

inverse oflaplace {(10)/(s(s+2))}

inverse laplace

{\frac{10}{s ( s + 2 )}}

5 H (t) - 5 e^{- 2 t}

Solution steps

L^{- 1} {\frac{10}{s ( s + 2 )}}

Take the partial fraction of

\frac{10}{s ( s + 2 )} : \frac{5}{s} - \frac{5}{s + 2}

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

L^{- 1} {\frac{5}{s}} : 5 H (t)

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

= 5 H (t) - 5 e^{- 2 t}

\frac{d}{d x} (7 (x^{3} - x)^{4})

\int (3 x^{4} - 5 x) d x

\frac{d}{d x} (6 x + 29 cos (\frac{3 x}{4}) + 5 x^{2} + 3)

\int (2 x - 3)^{5} d x

y \to x lim (\frac{y ^{\frac{2}{3}} - x ^{\frac{2}{3}}}{y - x})

What is inverse oflaplace {(10)/(s(s+2))} ?
The answer to inverse oflaplace {(10)/(s(s+2))} is 5\H(t)-5e^{-2t}