Past exam of the differential equations 1 course of the University of Oxford / 2017 / 2 / b / iii

Two solutions for $x\ge 2$ areFor the second, $y_2^{\prime }=-(x-2)/2=-\sqrt{|1+y_2|}$ because $x\ge 2$; both have value $-1$ and derivative zero at two. They are distinct for every $x>2$. Local Lipschitz continuity fails at the equilibrium, so the existence of these two continuations is compatible with the Picard-Lindelöf theorem.