inverselaplace (s-2)/((s-3)(s-1))

Lösung

inverse laplace transformation

\frac{s - 2}{( s - 3 ) ( s - 1 )}

\frac{1}{2} e^{3 t} + \frac{1}{2} e^{t}

Schritte zur Lösung

L^{- 1} {\frac{s - 2}{( s - 3 ) ( s - 1 )}}

Ermittle den Partialbruch von

\frac{s - 2}{( s - 3 ) ( s - 1 )} : \frac{1}{2 ( s - 3 )} + \frac{1}{2 ( s - 1 )}

= L^{- 1} {\frac{1}{2 ( s - 3 )} + \frac{1}{2 ( s - 1 )}}

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}{2 ( s - 3 )}} + L^{- 1} {\frac{1}{2 ( s - 1 )}}

L^{- 1} {\frac{1}{2 ( s - 3 )}} : \frac{1}{2} e^{3 t}

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

= \frac{1}{2} e^{3 t} + \frac{1}{2} e^{t}

\frac{d}{d x} (\frac{cos ( x ) - 1}{x})

\int_{1}^{3} \frac{5}{x ^{2} + 2 x + 1} d x

\int \frac{1}{200 - x} d x

d er i v a t i v e sin^{2} (e^{s i n^{2} (t)})

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1})