Solution
= Solution
Since $5y^2\leq9$, we have $y\in\{-1,0,1\}$. For $y=0$, $x^2=9$; for $y=\pm1$, $x^2=4$. Thus the solutions of the <Diophantine equation> are
$$
\boxed{(x,y)=(\pm3,0),(\pm2,\pm1),}
$$
where the two signs in the second family are independent.