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

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

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inverse oflaplace 2/(2s-1)

inverse laplace

\frac{2}{2 s - 1}

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

Solution steps

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

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

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)}

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

Use Inverse Laplace Transform table:

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

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

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

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

\frac{d}{d x} (5^{- \frac{x}{2}})

2 \cdot x

x \to 8 lim (7 (8 x + 5)^{3})

\int_{1}^{3} 3 d x

\int_{0}^{e} \frac{1}{x} d x

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