The general solution of $y = 2x \frac{dy}{dx} + y\left(\frac{dy}{dx}\right)^2$…

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The general solution of $y = 2x \frac{dy}{dx} + y\left(\frac{dy}{dx}\right)^2$ is

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Put $p = \frac{dy}{dx}$

$y = 2xp + yp^2$

$y(1 - p^2) = 2xp$

$y = \frac{2xp}{1 - p^2}$

This is Clairaut’s form. Hence general solution is

$2xc - y + c^2 = 0$

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