Solution
= Solution
Translation in $x$ leaves this autonomous <differential equation> unchanged. For every $c\ge1$, the same formula
$$
u_c(x)=\begin{cases}0,&x\le c,\\{}[3(x-c)/4]^{4/3},&x\ge c\end{cases}
$$
satisfies $u_c(1)=0$, and the zero function does too. Thus \b[solutions exist and are not unique], exactly as for the initial point $(0,0)$. The relevant failure is the <Lipschitz condition> at $y=0$; moving the initial value of $x$ does not remove it.