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Beliebt Rechnen >

laplacetransform 7+3t+2t^2-5t^3

Lösung

laplace transformation

7 + 3 t + 2 t^{2} - 5 t^{3}

Lösung

\frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

Schritte zur Lösung

L {7 + 3 t + 2 t^{2} - 5 t^{3}}

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)}

= L {7} + 3 L {t} + 2 L {t^{2}} - 5 L {t^{3}}

L {7} : \frac{7}{s}

L {t} : \frac{1}{s ^{2}}

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

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

= \frac{7}{s} + 3 \cdot \frac{1}{s ^{2}} + 2 \cdot \frac{2}{s ^{3}} - 5 \cdot \frac{6}{s ^{4}}

Fasse

\frac{7}{s} + 3 \frac{1}{s ^{2}} + 2 \frac{2}{s ^{3}} - 5 \frac{6}{s ^{4}}

zusammen:

\frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

= \frac{7}{s} + \frac{3}{s ^{2}} + \frac{4}{s ^{3}} - \frac{30}{s ^{4}}

Beliebte Beispiele

derivative of 4/(sqrt(x+7))

\frac{d}{d x} (\frac{4}{x + 7})

tangent y= 2/((x-2))

t an g e n t y = \frac{2}{( x - 2 )}

integral from 0 to 6 of pi(sqrt(x-1))^2

\int_{0}^{6} π (x - 1)^{2} d x

x^2y^'+8xy=17y^3

x^{2} y^{^{'}} + 8 x y = 17 y^{3}

integral of (2xarcsin(x))/(sqrt(1-x^2))

\int \frac{2 x arcsin ( x )}{1 - x ^{2}} d x