= Solution
The zero solution satisfies both the <ordinary differential equation> and the <initial condition>. The right-hand side is continuously differentiable in $y$ near $(x,y)=(2,0)$, so the <Picard-Lindelöf theorem> gives local uniqueness; equivalently the nonzero family in part (a) can never take the value zero at $x=2$. Thus
$$
\boxed{y(x)=0\quad\text{on }(0,\infty).}
$$
The restriction $x>0$ is the maximal <interval> containing $2$ on which the original <ordinary differential equation> is defined.
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