What is inverse oflaplace 1/(5s-2) ?

The answer to inverse oflaplace 1/(5s-2) is 1/5 e^{(2t)/5}

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inverse oflaplace 1/(5s-2)

inverse laplace

\frac{1}{5 s - 2}

\frac{1}{5} e^{\frac{2 t}{5}}

Solution steps

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

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

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

Use Inverse Laplace Transform table:

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

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

= \frac{1}{5} e^{\frac{2 t}{5}}

\int \frac{x ^{2}}{2 x} d x

\int c^{x} d x

x \to - 2 lim (4 x^{2} + 3 x - 1)

\int (6 x^{2} - 3 x + 5) d x

(- 1, 2), (1, - 1)

What is inverse oflaplace 1/(5s-2) ?
The answer to inverse oflaplace 1/(5s-2) is 1/5 e^{(2t)/5}