Which family of curves has the differential equation $\frac{dy}{dx} = \frac{y}{x}$?

Explanation

1. 01

   Separate: $\frac{dy}{y} = \frac{dx}{x}$, so $\log|y| = \log|x| + \log|C|$.

2. 02

   That is $y = Cx$: every line through the origin.