Abstract
We consider nonlinear ordinary differential equations up to the sixth order that are associated with the heat equation. Each of them is subjected to the Painleve analysis. For the fourth- and sixth-order equations we obtain a criterion for having the Painleve property; for the fifth-order equation we formulate necessary conditions for passing the Painleve test. We also present a fifth-order equation analogous to the Chazy-3 equation.
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