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Beliebt Rechnen >

(dy)/(dx)=(x-1)/(3x^2-6x-1)

Lösung

\frac{d y}{d x} = \frac{x - 1}{3 x ^{2} - 6 x - 1}

Lösung

y = \frac{1}{6} ln (3 x^{2} - 6 x - 1) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = \frac{x - 1}{3 x ^{2} - 6 x - 1}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = \frac{x - 1}{3 x ^{2} - 6 x - 1}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int \frac{x - 1}{3 x ^{2} - 6 x - 1} d x

\int \frac{x - 1}{3 x ^{2} - 6 x - 1} d x = \frac{1}{6} ln (3 x^{2} - 6 x - 1) + c_{1}

y = \frac{1}{6} ln (3 x^{2} - 6 x - 1) + c_{1}

Graph

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