What is inverse oflaplace (s*(s+3))/(s+2) ?

The answer to inverse oflaplace (s*(s+3))/(s+2) is \delta'(t)+\delta(t)-2e^{-2t}

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inverse oflaplace (s*(s+3))/(s+2)

inverse laplace

\frac{s \cdot ( s + 3 )}{s + 2}

δ' (t) + δ (t) - 2 e^{- 2 t}

Solution steps

L^{- 1} {\frac{s ( s + 3 )}{s + 2}}

Take the partial fraction of

\frac{s ( s + 3 )}{s + 2} : s + 1 - \frac{2}{s + 2}

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

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

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

L^{- 1} {s} : δ^{'} (t)

L^{- 1} {1} : δ (t)

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

= δ^{^{'}} (t) + δ (t) - 2 e^{- 2 t}

4 t^{3} sin (t)

x y^{^{'}} + y + y^{2} = 0, y (1) = 2

\frac{\partial}{\partial x} (\frac{1}{2} x y^{2})

x \to 0 lim (\frac{1 0 ^{x} - e ^{x}}{x})

x \to - \infty lim (\frac{x}{3})

What is inverse oflaplace (s*(s+3))/(s+2) ?
The answer to inverse oflaplace (s*(s+3))/(s+2) is \delta'(t)+\delta(t)-2e^{-2t}