It is not homogeneus, it is a separated variables equation.
So I'm stuck on:
(1-x²)y' = 1-y²
I think it's homogeneous but even that I'm not sure of. (I'm pretty new to first and second order ODEs so I'm finding it really hard at the moment!)
I simply took the (1-x²) to the other side to make it an equation in y'(x) but I have no idea on what to do now.
I know for homogeneous equations you can say that y=xv and let
y'(x) = xdv/dx + v for example but I can't get that to work here (suggesting that I might be wrong in thinking that it's a homogeneous equation....).
Any help is really appreciated!