What is inverse oflaplace ((-1/4))/(1+(1/2)*s) ?

The answer to inverse oflaplace ((-1/4))/(1+(1/2)*s) is -1/2 e^{-2t}

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inverse oflaplace ((-1/4))/(1+(1/2)*s)

inverse laplace

\frac{( - \frac{1}{4} )}{1 + ( \frac{1}{2} ) \cdot s}

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

Solution steps

L^{- 1} {\frac{( - \frac{1}{4} )}{1 + ( \frac{1}{2} ) s}}

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

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

Use Inverse Laplace Transform table:

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

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

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

\frac{d}{d x} ((arctan (x))^{2})

x \to 1 + lim (\frac{1}{x + 8})

\frac{\partial}{\partial x} (- 6 y sin (3 x))

\int \frac{1}{x 4 x ^{2} + 25} d x

y = 3 cos (x) sin (x)

What is inverse oflaplace ((-1/4))/(1+(1/2)*s) ?
The answer to inverse oflaplace ((-1/4))/(1+(1/2)*s) is -1/2 e^{-2t}