= Poles of a Riccati solution from zeros of its linearizing solution
{title2=$y\sim1/[c(t-t_*)]$}
At a regular point of a second-order <linear ordinary differential equation>, a nontrivial solution cannot have both $x$ and $x'$ zero, by initial-value uniqueness. Its zeros are therefore simple. Under the <linearization of a Riccati equation>, such a zero $t_*$ produces $y=x'/(cx)\sim1/[c(t-t_*)]$. Zeros separate the intervals on which the <Riccati equation> solution is finite.
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