Which differential equation does the family $y = Ax^2$ satisfy, $A$ being an arbitrary constant?

Explanation

1. 01

   $\frac{dy}{dx} = 2Ax$, and from the family $A = \frac{y}{x^2}$.

2. 02

   So $\frac{dy}{dx} = \frac{2y}{x}$, that is $x\frac{dy}{dx} = 2y$.