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June 1, 2021 Compiled on June 1, 2021 at 2:21am

1 The papers

1.1 An Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations (1985 version)

1.2 An Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations (2005 version)

1.3 An Implementation of Kovacic’s Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations

1.4 A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

1.5 Kovacic’s Algorithm and Its Application to Some Families of Special Functions

1.6 Note on Kovacic’s Algorithm

1.7 Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Diﬀerential Equations

1.8 How to Solve Linear Diﬀerential Equations: An Outline

1.9 Solving Second Order Linear Diﬀerential Equations with Klein’s Theorem

1.10 Liouvillian solutions for second order linear diﬀerential equations with polynomial coeﬃcients

1.11 A rationality result for Kovacic’s algorithm

1.12 NonLiouvillian Solutions for Second Order Linear ODEs

1.13 Galois Groups of Second and Third Order Linear Diﬀerential Equations

1.14 Liouvillian and Algebraic Solutions of Second and Third Order Linear Diﬀerential Equations

1.15 Algorithm implementation in FriCAS

These are collection of papers related to Kovacic algorithm for solving diﬀerential equations. As
I was studying the algorithm, I thought it will be good to have any related paper I ﬁnd on the
subject in one place for easy access. The HTML version has only the outlines. Only the PDF
version has the actual papers shown.
1.1 An Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations (1985 version)

1.2 An Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations (2005 version)

1.3 An Implementation of Kovacic’s Algorithm for Solving Second Order Linear Homogeneous Diﬀerential Equations

1.4 A DISCUSSION AND IMPLEMENTATION OF KOVACICS ALGORITHM FOR ORDINARY DIFFERENTIAL EQUATIONS

1.5 Kovacic’s Algorithm and Its Application to Some Families of Special Functions

1.6 Note on Kovacic’s Algorithm

1.7 Necessary Conditions for Liouvillian Solutions of (Third Order) Linear Diﬀerential Equations

1.8 How to Solve Linear Diﬀerential Equations: An Outline

1.9 Solving Second Order Linear Diﬀerential Equations with Klein’s Theorem

1.10 Liouvillian solutions for second order linear diﬀerential equations with polynomial coeﬃcients

1.11 A rationality result for Kovacic’s algorithm

1.12 NonLiouvillian Solutions for Second Order Linear ODEs

1.13 Galois Groups of Second and Third Order Linear Diﬀerential Equations

1.14 Liouvillian and Algebraic Solutions of Second and Third Order Linear Diﬀerential Equations

1.15 Algorithm implementation in FriCAS

The papers

This is the original paper by JERALD J. KOVACIC.

By JERALD J. KOVACIC.

By B. David Saunders

By Carolyn J. Smith.

By Anne Duval, and Michele Loday-Richaud.

By FELIX ULMER and JACQUES-ARTHUR WEIL

By FELIX ULMER and Michael F. Singer.

By FELIX ULMER

By Mark van Hoeij, Jacques-Arthur Weil and Thomas Cluzeau.

By Primitivo B. Acosta‑Humánez, David Blázquez‑Sanz, Henock Venegas‑Gómez

By Marius van der Put, Peter A. Hendriks

By L. Chan, E.S. Cheb-Terrab

By MICHAEL F. SINGER and FELIX ULMER. Journal of Symbolic Computation, 16, July 1993, 9 - 36

By MICHAEL F. SINGER and FELIX ULMER. Journal of Symbolic Computation, 16, July 1993, 37 - 74.

See https://github.com/fricas/fricas/blob/master/src/algebra/kovacic.spad