| Issue |
ITM Web Conf.
Volume 20, 2018
International Conference on Mathematics (ICM 2018) Recent Advances in Algebra, Numerical Analysis, Applied Analysis and Statistics
|
|
|---|---|---|
| Article Number | 01006 | |
| Number of page(s) | 6 | |
| Section | Algebra | |
| DOI | https://doi.org/10.1051/itmconf/20182001006 | |
| Published online | 12 October 2018 | |
An algebraic method for quasi-linear first-order ODEs
Fractional Calculus, Optimization and Algebra Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
*
e-mail: vongocthieu@tdtu.edu.vn
In this paper, we consider the class of quasi-linear first-order ODEs of the form y′ = P(x; y), where P is a polynomial in y with coefficients in ℂ(x), and study their algebraic solutions. Our method is intrinsically based on algebraic function field theory. We give an upper bound for the degrees of algebraic solutions which are in a quadratic extension of ℂ(x).
© The Authors, published by EDP Sciences, 2018
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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