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Beliebt Rechnen >

inverselaplace {1/(s^2+s-20)}

Lösung

inverse laplace transformation

{\frac{1}{s ^{2} + s - 20}}

Lösung

\frac{1}{9} e^{4 t} - \frac{1}{9} e^{- 5 t}

Schritte zur Lösung

L^{- 1} {\frac{1}{s ^{2} + s - 20}}

Ermittle den Partialbruch von

\frac{1}{s ^{2} + s - 20} : \frac{1}{9 ( s - 4 )} - \frac{1}{9 ( s + 5 )}

= L^{- 1} {\frac{1}{9 ( s - 4 )} - \frac{1}{9 ( s + 5 )}}

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}{9 ( s - 4 )}} - L^{- 1} {\frac{1}{9 ( s + 5 )}}

L^{- 1} {\frac{1}{9 ( s - 4 )}} : \frac{1}{9} e^{4 t}

L^{- 1} {\frac{1}{9 ( s + 5 )}} : \frac{1}{9} e^{- 5 t}

= \frac{1}{9} e^{4 t} - \frac{1}{9} e^{- 5 t}

Beliebte Beispiele

derivative of arcsin(1-2x^2)

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

derivative of e^x+x^2

\frac{d}{d x} (e^{x} + x^{2})

(\partial)/(\partial x)(45-x^2-y^2)

\frac{\partial}{\partial x} (45 - x^{2} - y^{2})

derivative of sin(2x-2pi)

\frac{d}{d x} (sin (2 x - 2 π))

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

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