Question

sin y(dy)/(dx) = cos(2cos y-sin^2x)

Answer 1

What are you looking to do here?

Answer 2

Hmm ... something tells me this is supposed to be a separable ODE. Try using some identities to rewrite the RHS so that you can write it as a product of functions of \(y\) and \(x\).

Here's what I've tried. Cosine angle sum/difference identity:
\[\cos(2\cos y-\sin^2x)=\cos(2\cos y)\cos(\sin^2x)+\sin(2\cos y)\sin(\sin^2x)\]
Double angle identities:
\[\cdots=\bigg(\cos^2(\cos y)-\sin^2(\cos y)\bigg)\cos(\sin^2x)+2\sin(\cos y)\cos(\cos y)\sin(\sin^2x)\]