The solution of the differential equation $(1+x) y \mathrm{~d} x+(1-y) x \mathrm{~d} y=0$ is

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Aicharya · Accepted Answer

$\begin{aligned} & (1+x) y \mathrm{~d} x+(1-y) x \mathrm{~d} y=0 \ & \Rightarrow \int \frac{1+x}{x} \mathrm{~d} x=\int \frac{y-1}{y} \mathrm{~d} y \ & \Rightarrow \log |x|+x=y-\log |y|+C \ & \Rightarrow \log (x y)+x-y=C\end{aligned}$

The solution of the differential equation $(1+x) y \mathrm{~d} x+(1-y) x \mathrm{~d} y=0$ is

Solution