What is inverse oflaplace 1/(s(s+1/15)) ?

The answer to inverse oflaplace 1/(s(s+1/15)) is 15\H(t)-15e^{-t/(15)}

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inverse oflaplace 1/(s(s+1/15))

inverse laplace

\frac{1}{s ( s + \frac{1}{15} )}

15 H (t) - 15 e^{- \frac{t}{15}}

Solution steps

L^{- 1} {\frac{1}{s ( s + \frac{1}{15} )}}

Take the partial fraction of

\frac{1}{s ( s + \frac{1}{15} )} : \frac{15}{s} - \frac{225}{15 s + 1}

= L^{- 1} {\frac{15}{s} - \frac{225}{15 s + 1}}

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{15}{s}} - L^{- 1} {\frac{225}{15 s + 1}}

L^{- 1} {\frac{15}{s}} : 15 H (t)

L^{- 1} {\frac{225}{15 s + 1}} : 15 e^{- \frac{t}{15}}

= 15 H (t) - 15 e^{- \frac{t}{15}}

n = 1 \sum \infty \frac{( e ^{n} )}{n !}

\int sin (x - 1) d x

x = 2 y^{2}, x = 4 - y^{2}

\frac{\partial}{\partial x} (\frac{z}{x})

\int \frac{( x ^{3} + 10 )}{x ^{3} - 2 x ^{2} + 5 x} d x

What is inverse oflaplace 1/(s(s+1/15)) ?
The answer to inverse oflaplace 1/(s(s+1/15)) is 15\H(t)-15e^{-t/(15)}