laplacetransform e^{17t}t^7

Lösung

laplace transformation

e^{17 t} t^{7}

\frac{5040}{( s - 17 ) ^{8}}

Schritte zur Lösung

L {e^{17 t} t^{7}}

Wende Laplace-Transformationstabelle an:

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

Für

e^{17 t} t^{7} : f (t) = e^{17 t}, k = 7

= (- 1)^{7} \frac{d ^{7}}{d s ^{7}} (L {e^{17 t}})

L {e^{17 t}} : \frac{1}{s - 17}

\frac{d ^{7}}{d s ^{7}} (\frac{1}{s - 17}) = - \frac{5040}{( s - 17 ) ^{8}}

= (- 1)^{7} (- \frac{5040}{( s - 17 ) ^{8}})

= \frac{5040}{( s - 17 ) ^{8}}

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