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Beliebt Rechnen >

inverselaplace (s-5)/(s^2+s-6)

Lösung

inverse laplace transformation

\frac{s - 5}{s ^{2} + s - 6}

Lösung

- \frac{3}{5} e^{2 t} + \frac{8}{5} e^{- 3 t}

Schritte zur Lösung

L^{- 1} {\frac{s - 5}{s ^{2} + s - 6}}

Ermittle den Partialbruch von

\frac{s - 5}{s ^{2} + s - 6} : - \frac{3}{5 ( s - 2 )} + \frac{8}{5 ( s + 3 )}

= L^{- 1} {- \frac{3}{5 ( s - 2 )} + \frac{8}{5 ( s + 3 )}}

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{3}{5 ( s - 2 )}} + L^{- 1} {\frac{8}{5 ( s + 3 )}}

L^{- 1} {\frac{3}{5 ( s - 2 )}} : \frac{3}{5} e^{2 t}

L^{- 1} {\frac{8}{5 ( s + 3 )}} : \frac{8}{5} e^{- 3 t}

= - \frac{3}{5} e^{2 t} + \frac{8}{5} e^{- 3 t}

Beliebte Beispiele

derivative of sin(xdx)

\frac{d}{d x} (sin (x) d x)

integral of xsqrt(3x-2)

\int x 3 x - 2 d x

derivative of (3x^{ln(3x)})

\frac{d}{d x} ((3 x)^{l n (3 x)})

integral of sin^{-3/2}(x)cos^3(x)

\int sin^{- \frac{3}{2}} (x) cos^{3} (x) d x

limit as x approaches-1 of 2x^2-5x+3

x \to - 1 lim (2 x^{2} - 5 x + 3)