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

The answer to inverse oflaplace s/(s-3) is \delta(t)+3e^{3t}

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inverse oflaplace s/(s-3)

inverse laplace

\frac{s}{s - 3}

δ (t) + 3 e^{3 t}

Solution steps

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

Take the partial fraction of

\frac{s}{s - 3} : 1 + \frac{3}{s - 3}

= L^{- 1} {1 + \frac{3}{s - 3}}

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} {1} + L^{- 1} {\frac{3}{s - 3}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{3}{s - 3}} : 3 e^{3 t}

= δ (t) + 3 e^{3 t}

\frac{d}{d x} (4 x - 3 ln (x))

x \to - 2 lim (∣ ln ∣ x + 2 ∣ ∣)

x^{2} + 2, - x, 0, 1

\int \frac{2 cot ( x ) - 3 sin ^{2} ( x )}{sin ( x )} d x

x \to \infty lim (\frac{2170}{1 + e ^{- 0.156 x}})

What is inverse oflaplace s/(s-3) ?
The answer to inverse oflaplace s/(s-3) is \delta(t)+3e^{3t}