I encountered the non-linear, first-order differential equation $$ y'^2 + \sin^2 y = f(x), $$ where $f(x)$ is: $$ f(x) = \frac{\sin^2 x}{A + B\cos x + C\cos^2 x} $$
Does anyone have an idea of how to solve the full equation, and whether even a closed-form solution is possible?