How to solve the differential equation $x^2 \cos{y} + \dfrac{dy}{dx} x \sin{y} =\sin^2y$, given in a competitive exam? How do I solve $x^2 \cos{y} + \dfrac{dy}{dx} x \sin{y} =\sin^2y$? I found the problem in a competitive exam.

$$x^2 \cos{y} + \dfrac{dy}{dx} x \sin{y} =\sin^2y$$
The change of function $Y(x)=\cos(y(x))$ leads to a Riccati ODE, then to a second order linear ODE.

HINT : Solving this second order linear ODE involves Bessel functions. 
