An algebraic method for quasi-linear first-order ODEs

An algebraic method for quasi-linear first-order ODEs

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...

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Veröffentlicht in:ITM web of conferences 2018, Vol.20, p.1006
1. Verfasser: Vo, Thieu N.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Field theory
Mathematical analysis
Polynomials
Upper bounds
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Zusammenfassung: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 ).
ISSN:2271-2097
2431-7578
2271-2097
DOI:10.1051/itmconf/20182001006