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Beliebt Rechnen >

laplacetransform f(t)=t^2e^{3t}

Lösung

laplace transformation

f (t) = t^{2} 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

derivative of (x^2^{1/2})

\frac{d}{d x} ((x^{2})^{\frac{1}{2}})

derivative of (2x+3/(x+2))

\frac{d}{d x} (\frac{2 x + 3}{x + 2})

derivative of x^3+x^2+x+1

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

integral of 1/((1+cos(x))^2)

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

integral of 1/(t+2)

\int \frac{1}{t + 2} d t