finding a unique solution

Nov 2009
State the region(s) in the xy-plane where the existence of a unique solution through any specified point is guaranteed.

\(\displaystyle y' = ln (1 - x^2 - y^2)\)

I know that I have to perform partial fractions on these but I'm rusty on how to go about solving the \(\displaystyle ln (1 - x^2 - y^2)\) part.