laplacetransform t*e^{-3t}

Lösung

laplace transformation

t \cdot e^{- 3 t}

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

Schritte zur Lösung

L {e^{- 3 t} t}

Wende Laplace-Transformationstabelle an:

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

Für

t e^{- 3 t} : f (t) = e^{- 3 t}, k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{- 3 t}})

L {e^{- 3 t}} : \frac{1}{s + 3}

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

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

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

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

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

\int_{a}^{b} \frac{1}{b - a} x d x

\int (e^{x} - 2 x^{2}) d x

x y^{^{'}} = x^{2} + 3 y