Differential Equations in Calculus?

Question

Show that xy^3 - (xy^3)(sinx) = 1 is an implicit solution to

dy/dx = (xcosx + sinx - 1)y/ 3(x-xsinx) ........ My proofs are not matching up

Answer 1

xy^3(1-sinx)=1 so y^3(1-sinx) +3xy^2*y´(1-sinx) +xy^3(-cos x)=0sodividing by y^2

y(1-sinx-x cosx)= 3x(sinx-1)y¨so y´=dy/dx= y(xcosx +sinx-1)/3x(1-sinx)

which we are lookin for