The slope of a curve at every point $(x, y)$ is $\frac{2y}{x}$, and the curve passes through $(1, 3)$. What is $y$ when $x = 2$?

Explanation

1. 01

   $\frac{dy}{y} = \frac{2\,dx}{x}$, so $\log|y| = 2\log|x| + \log|C|$: $y = Cx^2$.

2. 02

   Through $(1, 3)$: $C = 3$. At $x = 2$, $y = 12$.