Unique solution of differential equation

Question

For what initial conditions the following differential equation $y'=\sqrt {(1-x^2-y^2)}$ has unique solution?\ Is Picard–Lindelöf theorem used for solving? How I'm supposed to get to answer, please some help

Answer 1

Hint: you don't want to take the square root of a negative number. And for Lipschitz purposes, square root of $0$ may also be bad.