Elementary and Liouvillian solutions of linear differential equations

DOI10.1016/S0747-7171(86)80026-8zbMath0652.12016OpenAlexW2124423029MaRDI QIDQ1106886

James H. Davenport, Michael F. Singer

Publication date: 1986

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0747-7171(86)80026-8

zbMATH Keywords

algorithmlinear differential equationLiouvillian solutiondifferential field

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Differential algebra (12H05) Abstract differential equations (12H20) Software, source code, etc. for problems pertaining to field theory (12-04)

Related Items (7)

Comments on Rosenlicht’s Integration in Finite Terms ⋮ Differential and difference algebra ⋮ Liouvillian solutions of linear differential equations with Liouvillian coefficients ⋮ Corrigendum to: ``Liouvillian solutions of first order nonlinear differential equations ⋮ Consistent systems of linear differential and difference equations ⋮ Calculating the Galois group of \(L_1(L_2(y))=0,\) \(L_1, L_2\) completely reducible operators ⋮ Formal solutions of differential equations

Cites Work

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• Differential extension fields of exponential type
• On Liouville's theory of elementary functions
• Sur l'intégrabilite élémentaire de quelques classes d'expressions
• An Extension of Liouville’s Theorem on Integration in Finite Terms
• On Second Order Linear Differential Equations with Algebraic Solutions
• Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
• Solutions of Linear Differential Equations in Function Fields of One Variable
• The Problem of Integration in Finite Terms
• The solution of the problem of integration in finite terms
• An Analogue of L'Hospital's Rule

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