Q:

Seeking an analytic solution to a first order nonlinear ordinary differential equation

Does anyone have suggestions on how to tackle the following equation:
$$\left(\frac{dy}{dx}\right)^2 = B(\sin(y(x)))^2 - C\sin(y(x)) + D $$
The constants are real and nonzero 

A:

There are closed-form constant solutions (which may or may not be real, depending on the values of the parameters).  Otherwise, you need to integrate
$$  \int \dfrac{dy}{\sqrt{B \sin^2(y) - C \sin(y) + D}} $$
which seems not to be elementary in general: Maple gives a rather complicated antiderivative
in terms of EllipticF, which is the incomplete elliptic integral of the first kind.

