What is inverse oflaplace 9/(22(3s-2)) ?

The answer to inverse oflaplace 9/(22(3s-2)) is 3/22 e^{(2t)/3}

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inverse oflaplace 9/(22(3s-2))

inverse laplace

\frac{9}{22 ( 3 s - 2 )}

\frac{3}{22} e^{\frac{2 t}{3}}

Solution steps

L^{- 1} {\frac{9}{22 ( 3 s - 2 )}}

= L^{- 1} {\frac{3}{22} \cdot \frac{1}{s - \frac{2}{3}}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{3}{22} L^{- 1} {\frac{1}{s - \frac{2}{3}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s - \frac{2}{3}}} = e^{\frac{2 t}{3}}

= \frac{3}{22} e^{\frac{2 t}{3}}

What is inverse oflaplace 9/(22(3s-2)) ?
The answer to inverse oflaplace 9/(22(3s-2)) is 3/22 e^{(2t)/3}