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Question Number 180550 by a.lgnaoui last updated on 13/Nov/22

$$Resoudre$$$${af}^{{}^{\prime }}\left(x\right)+\frac{b}{f\left(x\right)}+c=0(a,b,c)\in {\mathbb{R}}^3$$

Answered by mr W last updated on 13/Nov/22

$$a\frac{dy}{dx}=-\frac{b+cy}{y}$$$$\frac{aydy}{b+cy}=-dx$$$$(1-\frac{b}{cy+b})dy=-\frac{c}{a}dx$$$$\int (1-\frac{b}{cy+b})dy=-\frac{c}{a}\int dx$$$$y-\frac{b}{c}\ln \mid cy+b\mid =-\frac{cx}{a}+k$$$$\Rightarrow y+\frac{cx}{a}-\frac{b}{c}\ln \mid cy+b\mid =k$$

Commented by a.lgnaoui last updated on 14/Nov/22

$$thanks$$

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