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Beliebt Rechnen >

inverselaplace 2/(s^3+3s^2-4)

Lösung

inverse laplace transformation

\frac{2}{s ^{3} + 3 s ^{2} - 4}

Lösung

\frac{2}{9} e^{t} - \frac{2}{9} e^{- 2 t} - \frac{2 e ^{- 2 t} t}{3}

Schritte zur Lösung

L^{- 1} {\frac{2}{s ^{3} + 3 s ^{2} - 4}}

Ermittle den Partialbruch von

\frac{2}{s ^{3} + 3 s ^{2} - 4} : \frac{2}{9 ( s - 1 )} - \frac{2}{9 ( s + 2 )} - \frac{2}{3 ( s + 2 ) ^{2}}

= L^{- 1} {\frac{2}{9 ( s - 1 )} - \frac{2}{9 ( s + 2 )} - \frac{2}{3 ( s + 2 ) ^{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{2}{9 ( s - 1 )}} - L^{- 1} {\frac{2}{9 ( s + 2 )}} - L^{- 1} {\frac{2}{3 ( s + 2 ) ^{2}}}

L^{- 1} {\frac{2}{9 ( s - 1 )}} : \frac{2}{9} e^{t}

L^{- 1} {\frac{2}{9 ( s + 2 )}} : \frac{2}{9} e^{- 2 t}

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

= \frac{2}{9} e^{t} - \frac{2}{9} e^{- 2 t} - \frac{2 e ^{- 2 t} t}{3}

Beliebte Beispiele

integral of e^{-0.25x}

\int e^{- 0.25 x} d x

laplacetransform 3cos^2(t)

l a pl a ce t r an s f or m 3 cos^{2} (t)

t^2y^{''}+4ty^'-10y=0

t^{2} y^{^{''}} + 4 t y^{^{'}} - 10 y = 0

(5x+ye^{y/x})dx-(xe^{y/x})dy=0,y(1)=3

(5 x + y e^{\frac{y}{x}}) d x - (x e^{\frac{y}{x}}) d y = 0, y (1) = 3

limit as t approaches 0 of (sin(t))/t

t \to 0 lim (\frac{sin ( t )}{t})