I'm working through the Brachistochrone Problem but I get stuck at the differential equation:

$\displaystyle (1+y'^2)y=K^2$ (eq. 13)

The solution is supposed to be in the form of two parametric functions $\displaystyle x(\theta)$ and $\displaystyle y(\theta)$, so I tried switching to polar coordinates and manipulating the equation in various ways. But that lead me to some hairy integrals, and I want to find out if I'm on the right track before I continue.

What's the best approach here?