On Liouvillian solutions of linear differential equations

DOI10.1007/BF01294332zbMath0752.12004MaRDI QIDQ1189716

Felix Ulmer

Publication date: 27 September 1992

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

zbMATH Keywords

Riccati equationminimal polynomialdifferential Galois groupLiouvillian solutionhomogeneous linear differential equation

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Linear ordinary differential equations and systems (34A30) Differential algebra (12H05)

Related Items

Absolute reducibility of differential operators and Galois groups ⋮ Necessary conditions for Liouvillian solutions of (third order) linear differential equations ⋮ Linear differential equations and products of linear forms ⋮ Algorithms and methods in differential algebra ⋮ Examples of the investigation of differential equations with modularized programs ⋮ On second order homogeneous linear differential equations with Liouvillian solutions ⋮ Rational solutions of Riccati differential equation with coefficients rational ⋮ Kovacic's algorithm and its application to some families of special functions

Uses Software

• Cayley

Cites Work

• An algorithm for solving second order linear homogeneous differential equations
• Liouvillian solutions of linear differential equations with Liouvillian coefficients
• Über endliche lineare Gruppen von Primzahlgrad. (On finite linear groups of prime number degree)
• Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations
• Solving Homogeneous Linear Differential Equations in Terms of Second Order Linear Differential Equations
• On Second Order Linear Differential Equations with Algebraic Solutions
• Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
• Finite Linear Groups of Prime Degree
• Endliche Gruppen I
• Groups Which Have a Faithful Representation of Degree Less Than p - 1
• On Groups Whose Order Contains a Prime Number to the First Power I
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