There's a couple ways to solve this but a simple straightforward one will work here. Since we have a derivative, if we isolate our y's we can integrate and then isolate for y.
So
[tex]y' = - y^{2} sinx[/tex]
to
[tex] y^{-2} y' = -sinx[/tex]
And just to understand we can integrate it, think about this in differential form to create
[tex] y^{-2} dy = -sinx dx[/tex]
And integrate!
