inverselaplace 2/(s^2(s^2+25))

Lösung

inverse laplace transformation

\frac{2}{s ^{2} ( s ^{2} + 25 )}

\frac{2 t}{25} - \frac{2}{125} sin (5 t)

Schritte zur Lösung

L^{- 1} {\frac{2}{s ^{2} ( s ^{2} + 25 )}}

Ermittle den Partialbruch von

\frac{2}{s ^{2} ( s ^{2} + 25 )} : \frac{2}{25 s ^{2}} - \frac{2}{25 ( s ^{2} + 25 )}

= L^{- 1} {\frac{2}{25 s ^{2}} - \frac{2}{25 ( s ^{2} + 25 )}}

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}{25 s ^{2}}} - L^{- 1} {\frac{2}{25 ( s ^{2} + 25 )}}

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

L^{- 1} {\frac{2}{25 ( s ^{2} + 25 )}} : \frac{2}{125} sin (5 t)

= \frac{2 t}{25} - \frac{2}{125} sin (5 t)

\frac{d}{d x} (5 x^{7} sin (x))

\frac{d y}{d t} = 0.3 y + 26 e^{0.3 t}

d er i v a t i v e \frac{8 x ^{2} + 4 x + 8}{x}

\int p (p + 5)^{7} d p

\int \frac{x}{x ^{2} + 6 x + 10} d x