Which differential equation describes the circles $x^2 + y^2 = 2ax$, with centre on the $x$-axis and passing through the origin?

Explanation

1. 01

   Differentiate: $2x + 2y\frac{dy}{dx} = 2a$, so $a = x + y\frac{dy}{dx}$.

2. 02

   Put this back: $x^2 + y^2 = 2x\left(x + y\frac{dy}{dx}\right)$, which gives $2xy\frac{dy}{dx} = y^2 - x^2$.