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Beliebt Rechnen >

laplacetransform (e^t-e^{-t})^2

Lösung

laplace transformation

(e^{t} - e^{- t})^{2}

Lösung

\frac{8}{s ( s - 2 ) ( s + 2 )}

Schritte zur Lösung

L {(e^{t} - e^{- t})^{2}}

Schreibe

(e^{t} - e^{- t})^{2}

um:

e^{2 t} - 2 + e^{- 2 t}

= L {e^{2 t} - 2 + e^{- 2 t}}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {e^{2 t}} - L {2} + L {e^{- 2 t}}

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

L {2} : \frac{2}{s}

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

= \frac{1}{s - 2} - \frac{2}{s} + \frac{1}{s + 2}

Vereinfache

\frac{1}{s - 2} - \frac{2}{s} + \frac{1}{s + 2} : \frac{8}{s ( s - 2 ) ( s + 2 )}

= \frac{8}{s ( s - 2 ) ( s + 2 )}

Beliebte Beispiele

integral of 512x^2cos(8x)

\int 512 x^{2} cos (8 x) d x

derivative of ln((sin(x)/x))

\frac{d}{d x} (ln (\frac{sin ( x )}{x}))

fläche y=4ln(x),y=xln(x)

a re a y = 4 ln (x), y = x ln (x)

limit as x approaches 4 of e^{3/(4-x)}

x \to 4 lim (e^{\frac{3}{4 - x}})

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

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