differential equation again::

rearranging the terms we get, sin y (dy/dx) - 2 cos x cos y= -1/2 (sin x sin 2x)
let z =-cos y => (dz/dx) = sin y (dy/dx)
...thus the equation becomes dz/dx + 2z cos x = 1/2 sinx sin 2x
this is of the form (dz/dx) + P(x) y =Q(x).....where P and Q are functions of (x)
here the IF (integrating factor) is e^{∫P(x) dx} = e^{∫cos x dx}
....now it is done with a bit more exercise !