de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

inverselaplace 1+4/(s(s+2))

Lösung

inverse laplace transformation

1 + \frac{4}{s ( s + 2 )}

Lösung

δ (t) + 2 H (t) - 2 e^{- 2 t}

Schritte zur Lösung

L^{- 1} {1 + \frac{4}{s ( s + 2 )}}

Ermittle den Partialbruch von

\frac{4}{s ( s + 2 )} : \frac{2}{s} - \frac{2}{s + 2}

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

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

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

L^{- 1} {1} : δ (t)

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

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

= δ (t) + 2 H (t) - 2 e^{- 2 t}

Beliebte Beispiele

integral of (x+3)/(x^2+8x-9)

\int \frac{x + 3}{x ^{2} + 8 x - 9} d x

(\partial)/(\partial y)(xysqrt(x^2+y^2))

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

integral of xsqrt(3x^2+4)

\int x 3 x^{2} + 4 d x

integral of (5x)/(x^2+1)

\int \frac{5 x}{x ^{2} + 1} d x

sum from n=1 to infinity of 1/(n3^n)

n = 1 \sum \infty \frac{1}{n 3 ^{n}}