Solve the differential equation of

Y-cos x(dy/dx)=y^2(1-sin x)(cos x)

divide both sides by –cosx. the equation then turns into the bernoullis form of differential eqn (you can google this term and read its wikipedia page). note that this form is directly convertible into first order linear differential eqn (dy/dx+Py=Q), which is easily solvable using integrating factor.