inverselaplace {1/(s^2)-1/s+1/(s-2)}

Lösung

inverse laplace transformation

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

t - H (t) + e^{2 t}

Schritte zur Lösung

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

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

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

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

= t - H (t) + e^{2 t}

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{6}})

x \to 0 lim (\frac{4 x}{x})

\frac{d}{d t} (d cos (t) + t^{2} sin (t))

\frac{d}{d x} (r (x) e^{r (x) x})

\frac{d}{d x} (\frac{sec ( x )}{7 + sec ( x )})