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Beliebt Rechnen >

laplacetransform t^2e^{at}

Lösung

laplace transformation

t^{2} \cdot e^{a \cdot t}

Lösung

\frac{2}{( s - a ) ^{3}}

Schritte zur Lösung

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

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

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

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

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

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

Beliebte Beispiele

t^2y^{''}+19ty^'+81y=0

t^{2} y^{^{''}} + 19 t y^{^{'}} + 81 y = 0

integral of sqrt(1+cot^2(x))

\int 1 + cot^{2} (x) d x

integral from 0 to 5 of |15-5t|

\int_{0}^{5} ∣ 15 - 5 t ∣ d t

derivative of f(xx^'(x))

\frac{d}{d x} (f (x) x^{^{'}} (x))

(\partial)/(\partial x)(ln(8x^2+3y^2+3))

\frac{\partial}{\partial x} (ln (8 x^{2} + 3 y^{2} + 3))