If $\frac{dy}{dx} = \frac{y}{x}$ and $y = 2$ when $x = 1$, what is $y$ when $x = 3$?

Explanation

1. 01

   Separating, $\log|y| = \log|x| + \log|C|$, so $y = Cx$.

2. 02

   $y(1) = 2$ gives $C = 2$: $y = 2x$, and $y(3) = 6$.