Differential equation of a parabola with vertex at origin and symmetr…

The correct answer is Option (2) → $2x\frac{dy}{dx}-y=0$

$y^2=4ax$  ....(1)

from (1) $\frac{y^2}{x}=4a$

differentiating wrt x

$2y\frac{dy}{dx}=4a$

$2y\frac{dy}{dx}=\frac{y^2}{x}$

so $2x\frac{dy}{dx}-y=0$