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Beliebt Rechnen >

inverselaplace 1/((s^4)(s-5))

Lösung

inverse laplace transformation

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

Lösung

- \frac{1}{625} H (t) - \frac{t}{125} - \frac{t ^{2}}{50} - \frac{t ^{3}}{30} + \frac{1}{625} e^{5 t}

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{1}{s ^{4} ( s - 5 )} : - \frac{1}{625 s} - \frac{1}{125 s ^{2}} - \frac{1}{25 s ^{3}} - \frac{1}{5 s ^{4}} + \frac{1}{625 ( s - 5 )}

= L^{- 1} {- \frac{1}{625 s} - \frac{1}{125 s ^{2}} - \frac{1}{25 s ^{3}} - \frac{1}{5 s ^{4}} + \frac{1}{625 ( 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}{625 s}} - L^{- 1} {\frac{1}{125 s ^{2}}} - L^{- 1} {\frac{1}{25 s ^{3}}} - L^{- 1} {\frac{1}{5 s ^{4}}} + L^{- 1} {\frac{1}{625 ( s - 5 )}}

L^{- 1} {\frac{1}{625 s}} : \frac{1}{625} H (t)

L^{- 1} {\frac{1}{125 s ^{2}}} : \frac{t}{125}

L^{- 1} {\frac{1}{25 s ^{3}}} : \frac{t ^{2}}{50}

L^{- 1} {\frac{1}{5 s ^{4}}} : \frac{t ^{3}}{30}

L^{- 1} {\frac{1}{625 ( s - 5 )}} : \frac{1}{625} e^{5 t}

= - \frac{1}{625} H (t) - \frac{t}{125} - \frac{t ^{2}}{50} - \frac{t ^{3}}{30} + \frac{1}{625} e^{5 t}

Beliebte Beispiele

integral of e^{4x+2}

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

integral of ((2x+7))/(x+3)

\int \frac{( 2 x + 7 )}{x + 3} d x

integral of (x+4)sin(npix)

\int (x + 4) sin (nπ x) d x

sum from n=1 to infinity of 8(1/4)^n

n = 1 \sum \infty 8 (\frac{1}{4})^{n}

(\partial)/(\partial x)(rcos(x)sin(y))

\frac{\partial}{\partial x} (r cos (x) sin (y))