If $\frac{dy}{dx} = \frac{x}{y}$ and $y = 3$ when $x = 0$, what is $y$ when $x = 4$?

Explanation

1. 01

   Separating and integrating gives the general solution; the condition $y(0) = 3$ fixes the constant.

2. 02

   The particular solution is $y = \sqrt{x^{2} + 9}$.

3. 03

   At $x = 4$: $y = 5$.