S sbankica Nov 2009 37 0 May 17, 2010 #1 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.

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.