Which of these lines through the origin is a solution of $\frac{dy}{dx} = \frac{2x^{2} + y^{2}}{3xy}$?

Explanation

1. 01

   On $y = mx$, $\frac{dy}{dx} = m$ and the right side is $\frac{2 + m^{2}}{3m}$; the line is a solution when these are equal.

2. 02

   $2 + m^{2} = 3m^{2}$ gives $m^{2} = 1$, so $y = x$ (and $y = -x$) are solutions.