The differential equation of the family of parabola y^2=4ax where a i…

The correct answer is Option (1) → $2x\frac{dy}{dx}= y $

$y^2=4ax$ No. of arbitrary constants = 1 → order = 1

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

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

$⇒2x\frac{dy}{dx}=y$