Resoudre-af-x-b-f-x-c-0-a-b-c-R-3-

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

R e s o u d r e

{a f}^{^{'}} (x) + \frac{b}{f (x)} + c = 0 (a, b, c) \in R^{3}

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

a \frac{d y}{d x} = - \frac{b + c y}{y}

\frac{a y d y}{b + c y} = - d x

(1 - \frac{b}{c y + b}) d y = - \frac{c}{a} d x

\int (1 - \frac{b}{c y + b}) d y = - \frac{c}{a} \int d x

y - \frac{b}{c} \ln ∣ c y + b ∣= - \frac{c x}{a} + k

\Rightarrow y + \frac{c x}{a} - \frac{b}{c} \ln ∣ c y + b ∣= k

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

t h a n k s