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Beliebt Rechnen >

laplacetransform t^2*e^{3t}

Lösung

laplace transformation

t^{2} \cdot e^{3 t}

Lösung

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

Schritte zur Lösung

L {e^{3 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^{3 t} : f (t) = e^{3 t}, k = 2

= (- 1)^{2} \frac{d ^{2}}{d s ^{2}} (L {e^{3 t}})

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

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

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

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

Beliebte Beispiele

integral of tcos(t)

\int t cos (t) d t

tangent ln(x^3)

t an g e n t ln (x^{3})

integral of (x^2)/(2+x^6)

\int \frac{x ^{2}}{2 + x ^{6}} d x

steigung (-14,-11),(-12,11)

s l o p e (- 14, - 11), (- 12, 11)

derivative of ((3x+3/(x-5))^5)

\frac{d}{d x} ((\frac{3 x + 3}{x - 5})^{5})