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Beliebt Rechnen >

laplacetransform t^2e^{-2t}

Lösung

laplace transformation

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

Lösung

\frac{2}{( s + 2 ) ^{3}}

Schritte zur Lösung

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

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t^{2} e^{- 2 t} : f (t) = e^{- 2 t}, k = 2

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

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

\frac{d ^{2}}{d s ^{2}} (\frac{1}{s + 2}) = \frac{2}{( s + 2 ) ^{3}}

= (- 1)^{2} \frac{2}{( s + 2 ) ^{3}}

= \frac{2}{( s + 2 ) ^{3}}

Beliebte Beispiele

limit as x approaches 0 of e^0cos(4)(0)

x \to 0 lim (e^{0} cos (4) (0))

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

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

y^'=e^{2x}(1+y^2)

y^{^{'}} = e^{2 x} (1 + y^{2})

integral of y^2-2x

\int y^{2} - 2 x d x

integral of xe^{-8x}

\int x e^{- 8 x} d x