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Beliebt Rechnen >

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

Lösung

inverse laplace transformation

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

Lösung

- \frac{1}{4} e^{t} + \frac{e ^{t} t}{2} + \frac{1}{4} e^{- t}

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

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

= - \frac{1}{4} e^{t} + \frac{e ^{t} t}{2} + \frac{1}{4} e^{- t}

Beliebte Beispiele

integral of ((x^3+64))/(x^2+64)

\int \frac{( x ^{3} + 64 )}{x ^{2} + 64} d x

integral from 0 to 7 of 1

\int_{0}^{7} 1

derivative (x(x^2+4))^{1/3}

d er i v a t i v e (x (x^{2} + 4))^{\frac{1}{3}}

(\partial)/(\partial x)(sqrt(6+3x^2-2y^2))

\frac{\partial}{\partial x} (6 + 3 x^{2} - 2 y^{2})

integral of 4x^2+1/((2x)^2)

\int 4 x^{2} + \frac{1}{( 2 x ) ^{2}} d x