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Beliebt Rechnen >

laplacetransform 2(t-2)^2+6(t-2)+6

Lösung

laplace transformation

2 (t - 2)^{2} + 6 (t - 2) + 6

Lösung

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

Schritte zur Lösung

L {2 (t - 2)^{2} + 6 (t - 2) + 6}

Schreibe

2 (t - 2)^{2} + 6 (t - 2) + 6

um:

2 t^{2} - 2 t + 2

= L {2 t^{2} - 2 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)}

= 2 L {t^{2}} - 2 L {t} + L {2}

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

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

L {2} : \frac{2}{s}

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

Fasse

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

zusammen:

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

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

Beliebte Beispiele

integral of 1/(sqrt(4x^2-16))

\int \frac{1}{4 x ^{2} - 16} d x

integral of 2/(x^2-4x+13)

\int \frac{2}{x ^{2} - 4 x + 13} d x

sum from n=0 to infinity of 1/(n^4)

n = 0 \sum \infty \frac{1}{n ^{4}}

(dy)/(dx)+3x^2y=18x^2,y(0)=8

\frac{d y}{d x} + 3 x^{2} y = 18 x^{2}, y (0) = 8

derivative 38(4e^{x^2}x^3+6e^{x^2}x)

d er i v a t i v e 38 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)