laplacetransform 12t^3-t^2

Lösung

laplace transformation

12 t^{3} - t^{2}

\frac{72}{s ^{4}} - \frac{2}{s ^{3}}

Schritte zur Lösung

L {12 t^{3} - t^{2}}

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)}

= 12 L {t^{3}} - L {t^{2}}

L {t^{3}} : \frac{6}{s ^{4}}

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

= 12 \cdot \frac{6}{s ^{4}} - \frac{2}{s ^{3}}

Fasse

12 \frac{6}{s ^{4}} - \frac{2}{s ^{3}}

zusammen:

\frac{72}{s ^{4}} - \frac{2}{s ^{3}}

= \frac{72}{s ^{4}} - \frac{2}{s ^{3}}

\frac{d}{d x} (2 x - \frac{4}{x})

\int \frac{x ^{2}}{81 + x ^{2}} d x

\int_{0}^{1} sin (π \cdot x) d x

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5 x (x + 6 y) y^{^{'}} = 5 y (x - 6 y)