What is inverse oflaplace (12s+5)/(s(s+3)) ?

The answer to inverse oflaplace (12s+5)/(s(s+3)) is 5/3 \H(t)+31/3 e^{-3t}

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inverse oflaplace (12s+5)/(s(s+3))

inverse laplace

\frac{12 s + 5}{s ( s + 3 )}

\frac{5}{3} H (t) + \frac{31}{3} e^{- 3 t}

Solution steps

L^{- 1} {\frac{12 s + 5}{s ( s + 3 )}}

Take the partial fraction of

\frac{12 s + 5}{s ( s + 3 )} : \frac{5}{3 s} + \frac{31}{3 ( s + 3 )}

= L^{- 1} {\frac{5}{3 s} + \frac{31}{3 ( s + 3 )}}

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}{3 s}} + L^{- 1} {\frac{31}{3 ( s + 3 )}}

L^{- 1} {\frac{5}{3 s}} : \frac{5}{3} H (t)

L^{- 1} {\frac{31}{3 ( s + 3 )}} : \frac{31}{3} e^{- 3 t}

= \frac{5}{3} H (t) + \frac{31}{3} e^{- 3 t}

\frac{\partial}{\partial x} (x (1 - x))

x \to π lim (tan (\frac{x}{3}))

\int_{0}^{2} \frac{x}{1 + x ^{2}} d x

x \to 9 lim (\frac{x - 3}{x - 9})

25 x^{2}, 9

What is inverse oflaplace (12s+5)/(s(s+3)) ?
The answer to inverse oflaplace (12s+5)/(s(s+3)) is 5/3 \H(t)+31/3 e^{-3t}