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

The answer to inverse oflaplace-2/(s(s-1)+2) is -4/(sqrt(7))e^{t/2}sin((sqrt(7)t)/2)

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

inverse laplace

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

- \frac{4}{7} e^{\frac{t}{2}} sin (\frac{7 t}{2})

Solution steps

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

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

L^{- 1} {\frac{1}{s ( s - 1 ) + 2}} : e^{\frac{t}{2}} \frac{2}{7} sin (\frac{7 t}{2})

= - 2 e^{\frac{t}{2}} \frac{2}{7} sin (\frac{7 t}{2})

Refine

- 2 e^{\frac{t}{2}} \frac{2}{7} sin (\frac{7 t}{2}) : - \frac{4}{7} e^{\frac{t}{2}} sin (\frac{7 t}{2})

= - \frac{4}{7} e^{\frac{t}{2}} sin (\frac{7 t}{2})

y = 2 x e^{- k x}

(- 3 x + 14)^{\frac{4}{3}}

\int (x^{2} y - ln (cos (x))) d y

\int \frac{1}{x 2 x - 1} d x

y = x (x - 10)

What is inverse oflaplace-2/(s(s-1)+2) ?
The answer to inverse oflaplace-2/(s(s-1)+2) is -4/(sqrt(7))e^{t/2}sin((sqrt(7)t)/2)