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Beliebt Rechnen >

inverselaplace 7/(s^2-9)

Lösung

inverse laplace transformation

\frac{7}{s ^{2} - 9}

Lösung

- \frac{7}{6} e^{- 3 t} + \frac{7}{6} e^{3 t}

Schritte zur Lösung

L^{- 1} {\frac{7}{s ^{2} - 9}}

Ermittle den Partialbruch von

\frac{7}{s ^{2} - 9} : - \frac{7}{6 ( s + 3 )} + \frac{7}{6 ( s - 3 )}

= L^{- 1} {- \frac{7}{6 ( s + 3 )} + \frac{7}{6 ( 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{7}{6 ( s + 3 )}} + L^{- 1} {\frac{7}{6 ( s - 3 )}}

L^{- 1} {\frac{7}{6 ( s + 3 )}} : \frac{7}{6} e^{- 3 t}

L^{- 1} {\frac{7}{6 ( s - 3 )}} : \frac{7}{6} e^{3 t}

= - \frac{7}{6} e^{- 3 t} + \frac{7}{6} e^{3 t}

Beliebte Beispiele

integral from-1 to 1 of f(x)

\int_{- 1}^{1} f (x) d x

integral of (2x-x^2)

\int (2 x - x^{2}) d x

limit as x approaches 0 of [x^2]-[x^3]

x \to 0 lim ([x^{2}] - [x^{3}])

derivative of (-1^x)

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

integral of x^2e^{x+4}

\int x^{2} e^{x + 4} d x