What is inverse oflaplace 3/(5s-2) ?

The answer to inverse oflaplace 3/(5s-2) is 3/5 e^{(2t)/5}

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inverse oflaplace 3/(5s-2)

inverse laplace

\frac{3}{5 s - 2}

\frac{3}{5} e^{\frac{2 t}{5}}

Solution steps

L^{- 1} {\frac{3}{5 s - 2}}

= L^{- 1} {\frac{3}{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{3}{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{3}{5} e^{\frac{2 t}{5}}

\int \frac{2 x + 1}{x ^{3} - x ^{2}} d x

\frac{\partial}{\partial x} (- x y z^{2} + 6)

\frac{d}{d x} (x sin (π) x)

x \to 0 + lim (x ln (x^{3}))

\frac{\partial}{\partial x} (\frac{2 x ^{2}}{y ^{2} + x ^{2}})

What is inverse oflaplace 3/(5s-2) ?
The answer to inverse oflaplace 3/(5s-2) is 3/5 e^{(2t)/5}