= Solution
Suppose there were no singular point in the <Riemann sphere>. Then every finite point would be ordinary, so $p$ and $q$ would be <entire functions>. Ordinary behavior at infinity would force $p(z)=2/z+O(z^{-2})$ and $q(z)=O(z^{-4})$. In particular $p(z)\to0$, so <Liouville theorem> would give $p\equiv0$, contradicting the required leading term $2/z$. Thus infinity cannot also be ordinary, and every such differential equation has at least one singular point in $\overline{\mathbb C}$.
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