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

Lösung

inverse laplace transformation

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

2 e^{- t} - 2 e^{- 2 t} - e^{- 2 t} \cdot 2 t

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

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

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

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

= 2 e^{- t} - 2 e^{- 2 t} - e^{- 2 t} \cdot 2 t

\frac{d y}{d x} = - \frac{e ^{x} y ^{2}}{10}

\int 3 ln^{2} (x) d x

\frac{d y}{d t} (t) - 2 y = 3 e^{t}

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

\frac{d}{d x} (1000 (1 - \frac{x}{500})^{2})