What is inverse oflaplace (10/6)/(s+6) ?

The answer to inverse oflaplace (10/6)/(s+6) is (5e^{-6t})/3

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inverse oflaplace (10/6)/(s+6)

inverse laplace

\frac{\frac{10}{6}}{s + 6}

\frac{5 e ^{- 6 t}}{3}

Solution steps

L^{- 1} {\frac{\frac{10}{6}}{s + 6}}

= L^{- 1} {\frac{10}{6} \cdot \frac{1}{s + 6}}

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{10}{6} L^{- 1} {\frac{1}{s + 6}}

Use Inverse Laplace Transform table:

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

L^{- 1} {\frac{1}{s + 6}} = e^{- 6 t}

= \frac{10}{6} e^{- 6 t}

= \frac{5 e ^{- 6 t}}{3}

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What is inverse oflaplace (10/6)/(s+6) ?
The answer to inverse oflaplace (10/6)/(s+6) is (5e^{-6t})/3