Solution
= Solution
By the transformed equation, infinity is ordinary precisely when
$$
\frac2t-\frac{p(1/t)}{t^2},
\qquad
\frac{q(1/t)}{t^4}
$$
are holomorphic at $t=0$. Equivalently, as convergent Laurent expansions near infinity,
$$
\boxed{p(z)=\frac2z+O(z^{-2}),
\qquad
q(z)=O(z^{-4}).}
$$