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Beliebt Rechnen >

(2x-1)dx+(3x+7)dy=0

Lösung

(2 x - 1) d x + (3 x + 7) d y = 0

Lösung

y = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

Schritte zur Lösung

(2 x - 1) d x + (3 x + 7) d y = 0

Lass

y

die abhängige Variable sein. Teile durch

d x

:

2 x - 1 + (3 x + 7) \frac{d y}{d x} = 0

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

2 x - 1 + (3 x + 7) y^{^{'}} (x) = 0

Isoliere

y^{'} (x) : y^{'} (x) = \frac{- 2 x + 1}{3 x + 7}

Wenn

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

dann

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

y = \int \frac{- 2 x + 1}{3 x + 7} d x

\int \frac{- 2 x + 1}{3 x + 7} d x = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

y = - \frac{2}{3} x + \frac{17}{9} ln (3 x + 7) + c_{1}

Graph

Beliebte Beispiele

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