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Beliebt Rechnen >

inverselaplace (s^2-1)/((s-2)^6)

Lösung

inverse laplace transformation

\frac{s ^{2} - 1}{( s - 2 ) ^{6}}

Lösung

\frac{e ^{2 t} t ^{3}}{6} + \frac{e ^{2 t} t ^{4}}{6} + \frac{e ^{2 t} t ^{5}}{40}

Schritte zur Lösung

L^{- 1} {\frac{s ^{2} - 1}{( s - 2 ) ^{6}}}

Ermittle den Partialbruch von

\frac{s ^{2} - 1}{( s - 2 ) ^{6}} : \frac{1}{( s - 2 ) ^{4}} + \frac{4}{( s - 2 ) ^{5}} + \frac{3}{( s - 2 ) ^{6}}

= L^{- 1} {\frac{1}{( s - 2 ) ^{4}} + \frac{4}{( s - 2 ) ^{5}} + \frac{3}{( s - 2 ) ^{6}}}

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}{( s - 2 ) ^{4}}} + L^{- 1} {\frac{4}{( s - 2 ) ^{5}}} + L^{- 1} {\frac{3}{( s - 2 ) ^{6}}}

L^{- 1} {\frac{1}{( s - 2 ) ^{4}}} : \frac{e ^{2 t} t ^{3}}{6}

L^{- 1} {\frac{4}{( s - 2 ) ^{5}}} : \frac{e ^{2 t} t ^{4}}{6}

L^{- 1} {\frac{3}{( s - 2 ) ^{6}}} : \frac{e ^{2 t} t ^{5}}{40}

= \frac{e ^{2 t} t ^{3}}{6} + \frac{e ^{2 t} t ^{4}}{6} + \frac{e ^{2 t} t ^{5}}{40}

Beliebte Beispiele

(dy)/(dx)+20y=sin(x)

\frac{d y}{d x} + 20 y = sin (x)

derivative of 3arctan(x)

\frac{d}{d x} (3 arctan (x))

(d^3)/(dx^3)((x^2-1)^3)

\frac{d ^{3}}{d x ^{3}} ((x^{2} - 1)^{3})

integral from 0 to pi/2 of 15cos^5(x)

\int_{0}^{\frac{π}{2}} 15 cos^{5} (x) d x

limit as x approaches-2+of-1/(x^2-4)

x \to - 2 + lim (- \frac{1}{x ^{2} - 4})