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Beliebt Rechnen >

laplacetransform 2(t-2)^2+7(t-2)+9

Lösung

laplace transformation

2 (t - 2)^{2} + 7 (t - 2) + 9

Lösung

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

Schritte zur Lösung

L {2 (t - 2)^{2} + 7 (t - 2) + 9}

Schreibe

2 (t - 2)^{2} + 7 (t - 2) + 9

um:

2 t^{2} - t + 3

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

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

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

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

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

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

Fasse

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

zusammen:

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

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

Beliebte Beispiele

derivative of sin(2x^3+x^2+1)

\frac{d}{d x} (sin (2 x^{3} + x^{2} + 1))

limit as x approaches 0 of (ax-aln(x+1))/(xln(x+1))

x \to 0 lim (\frac{a x - a ln ( x + 1 )}{x ln ( x + 1 )})

integral from 2 to 10 of 1/x

\int_{2}^{10} \frac{1}{x} d x

derivative of xe^{(2x})

\frac{d}{d x} (x e^{(2 x)})

(\partial)/(\partial x)(9sqrt(x^2+y^2))

\frac{\partial}{\partial x} (9 x^{2} + y^{2})