That does not matter: either the solutions are unique or not, and ODEs (out of singular points) have a unique aolution for any set of initial conditions.
The sensitivity to initial conditions has nothing to do with regular ODEs and uniqueness.
> ODEs (out of singular points) have a unique solution for any set of initial conditions
I am not sure if that statement is to weak. In general you can only guarantee the solution of an explicit ODE over some interval if the right hand side is Lipschitz continuous.
