On the polynomial solutions of the polynomial differential equations \({y \; y}' = a_0(x) + a_1(x) y + a_2(x) y^2 + \ldots + a_n(x) y^{n}\) (Q1985930)
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scientific article; zbMATH DE number 7187890
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the polynomial solutions of the polynomial differential equations \({y \; y}' = a_0(x) + a_1(x) y + a_2(x) y^2 + \ldots + a_n(x) y^{n}\) |
scientific article; zbMATH DE number 7187890 |
Statements
On the polynomial solutions of the polynomial differential equations \({y \; y}' = a_0(x) + a_1(x) y + a_2(x) y^2 + \ldots + a_n(x) y^{n}\) (English)
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7 April 2020
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The study of special solutions (as polynomial or rational solutions) of differential equations is of main interest. In this paper, the authors consider differential equations of the form \[yy'=a_{0}(x)+a_{1}(x)y+a_{2}(x)y^{2}+\cdots+a_{n}(x)y^{n}.\] They provide an upper bound for the number of polynomial solutions of this class of differential equations, and for some particular classes they study properties of their polynomial solutions.
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polynomial differential equation
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polynomial solution
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Riccati differential equation
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Abel differential equation
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