On Liouvillian solutions of linear differential equations
type: Item
instance of: scholarly article
title: On Liouvillian solutions of linear differential equations
zbMATH Open document ID: 0752.12004
DOI: 10.1007/BF01294332
author: Felix Ulmer
published in: Applicable Algebra in Engineering, Communication and Computing
publication date: 1992-09-27T00:00:00Z
review text: Let \(L(y)=0\) be a homogeneous linear differential equation and \(R(z)=0\) be the associated Riccati equation. The paper deals with the problem of finding the possible degrees of the minimal polynomial of an algebraic solution of \(R(z)=0\). Supposing that \(L(y)\) is irreducible and \(L(y)=0\) has a Liouvillian solution, the author obtains sharp bounds for the above degrees and solves the problem completely when the order of \(L(y)\) is 3. This information may be useful for setting up an algorithm like \textit{J. Kovacic'} algorithm [J. Symb. Comput. 2, 3-43 (1986; Zbl 0603.68035)]. For references on this subject see \textit{M. F. Singer} [J. Symb. Comput. 11, No. 3, 251-273 (1991)].
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 57749
zbMATH Keywords: differential Galois group
zbMATH Keywords: homogeneous linear differential equation
zbMATH Keywords: Riccati equation
zbMATH Keywords: minimal polynomial
zbMATH Keywords: Liouvillian solution
reviewed by: Mykola Grygorenko
describes a project that uses: Cayley
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 57749