What is inverse oflaplace s/(s+10^4) ?

The answer to inverse oflaplace s/(s+10^4) is \delta(t)-10000e^{-10000t}

inverse oflaplace s/(s+10^4)

inverse laplace

\frac{s}{s + 1 0 ^{4}}

δ (t) - 10000 e^{- 10000 t}

Solution steps

L^{- 1} {\frac{s}{s + 1 0 ^{4}}}

Take the partial fraction of

\frac{s}{s + 1 0 ^{4}} : 1 - \frac{10000}{s + 10000}

= L^{- 1} {1 - \frac{10000}{s + 10000}}

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{10000}{s + 10000}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{10000}{s + 10000}} : 10000 e^{- 10000 t}

= δ (t) - 10000 e^{- 10000 t}

\int_{1}^{e^{2}} \frac{ln ^{7} ( x ^{2} )}{x} d x

\frac{d}{d x} (x - sin (x))

d er i v a t i v e arctan (5 x)

\frac{d y}{d x} = x - x^{2}

d er i v a t i v e f (x) = sin (x) + cos (x)

What is inverse oflaplace s/(s+10^4) ?
The answer to inverse oflaplace s/(s+10^4) is \delta(t)-10000e^{-10000t}