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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

inverse oflaplace s/(s+4)

inverse laplace

\frac{s}{s + 4}

δ (t) - 4 e^{- 4 t}

Solution steps

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

Take the partial fraction of

\frac{s}{s + 4} : 1 - \frac{4}{s + 4}

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

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{4}{s + 4}}

L^{- 1} {1} : δ (t)

L^{- 1} {\frac{4}{s + 4}} : 4 e^{- 4 t}

= δ (t) - 4 e^{- 4 t}

\frac{d y}{d x} = \frac{1}{x + y}

\frac{\partial}{\partial x} (5 x^{2} y - 5 x + 4 y^{3})

\int x^{2} (e^{x}) d x

x \to - 2 lim (\frac{2 x + 2}{x - 1})

\frac{6 x}{1 - tan ( x )}

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