In this paper we deal with differential equations of the form yy′ = P(x, y) where y′ = dy/dx and P(x, y) is a polynomial in the variables x and y of degree n in the variable y. We provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes we study properties of their polynomial solutions.

中文翻译：

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关于多项式微分方程yy′= a 0（x）+ a 1（x）y + a 2（x）y 2 +…+ an（x）yn的多项式解

在本文中，我们处理的形式的微分方程YY '= P（X，ÿ）其中Ŷ '= DY / DX和P（X，Ý）是变量多项式X和ÿ度Ñ在可变ÿ。我们为这类微分方程的多项式解提供了一个上限，对于某些特定的类，我们研究了它们的多项式解的性质。