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Beliebt Rechnen >

laplacetransform 5t^2-2e^t

Lösung

laplace transformation

5 t^{2} - 2 e^{t}

Lösung

\frac{10}{s ^{3}} - \frac{2}{s - 1}

Schritte zur Lösung

L {5 t^{2} - 2 e^{t}}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= 5 L {t^{2}} - 2 L {e^{t}}

L {t^{2}} : \frac{2}{s ^{3}}

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

= 5 \cdot \frac{2}{s ^{3}} - 2 \cdot \frac{1}{s - 1}

Fasse

5 \frac{2}{s ^{3}} - 2 \frac{1}{s - 1}

zusammen:

\frac{10}{s ^{3}} - \frac{2}{s - 1}

= \frac{10}{s ^{3}} - \frac{2}{s - 1}

Beliebte Beispiele

derivative of-k/(x^2)

\frac{d}{d x} (- \frac{k}{x ^{2}})

derivative x^3-8x^2+19x-12

d er i v a t i v e x^{3} - 8 x^{2} + 19 x - 12

integral from 5 to 10 of (3x+3)

\int_{5}^{10} (3 x + 3) d x

integral of 1/(t^3+t^2-2t)

\int \frac{1}{t ^{3} + t ^{2} - 2 t} d t

integral of (32x^2)/((x-15)(x+5)^2)

\int \frac{32 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}} d x