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Beliebt Rechnen >

laplacetransform e^{-3t}+3+2t+4t^2+5t^3

Lösung

laplace transformation

e^{- 3 t} + 3 + 2 t + 4 t^{2} + 5 t^{3}

Lösung

\frac{1}{s + 3} + \frac{3}{s} + \frac{2}{s ^{2}} + \frac{8}{s ^{3}} + \frac{30}{s ^{4}}

Schritte zur Lösung

L {e^{- 3 t} + 3 + 2 t + 4 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 {e^{- 3 t}} + L {3} + 2 L {t} + 4 L {t^{2}} + 5 L {t^{3}}

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

L {3} : \frac{3}{s}

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

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

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

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

Fasse

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

zusammen:

\frac{1}{s + 3} + \frac{3}{s} + \frac{2}{s ^{2}} + \frac{8}{s ^{3}} + \frac{30}{s ^{4}}

= \frac{1}{s + 3} + \frac{3}{s} + \frac{2}{s ^{2}} + \frac{8}{s ^{3}} + \frac{30}{s ^{4}}

Beliebte Beispiele

derivative of sin(2x+cos(x))

\frac{d}{d x} (sin (2 x) + cos (x))

integral of cos(x/(sqrt(2)))

\int cos (\frac{x}{2}) d x

(1 + x) d y - y d x = 0

limit as x approaches infinity of 6^x

x \to \infty lim (6^{x})

limit as x approaches 0-of f(x)

x \to 0 - lim (f (x))