January 1, 2022 Compiled on January 1, 2022 at 9:05am

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 Liouvillian Solutions of Linear Diﬀerential Equations with Liouvillian Coeﬃcients

1.12 A rationality result for Kovacic’s algorithm

1.13 NonLiouvillian Solutions for Second Order Linear ODEs

1.14 Galois Groups of Second and Third Order Linear Diﬀerential Equations

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

1.16 Symbolic analysis of second-order ordinary diﬀerential equations with polynomial coeﬃcients

1.17 AN INTRODUCTION TO DIFFERENTIAL GALOIS THEORY

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

1.19 Formal Solutions of Diﬀerential Equations

1.20 ON SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH ALGEBRAIC SOLUTIONS

1.21 On second order homogeneous linear diﬀerential equations with Liouvillian solutions

1.22 Solutions of linear ordinary diﬀerential equations in terms of special functions

1.23 AN IMPLEMENTATION OF KOVACIC’S ALGORITHM FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS IN FORMAC

1.24 Algorithm implementation in FriCAS

1.25 Maxima implementation of Kovacic algorithm

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 Liouvillian Solutions of Linear Diﬀerential Equations with Liouvillian Coeﬃcients

1.12 A rationality result for Kovacic’s algorithm

1.13 NonLiouvillian Solutions for Second Order Linear ODEs

1.14 Galois Groups of Second and Third Order Linear Diﬀerential Equations

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

1.16 Symbolic analysis of second-order ordinary diﬀerential equations with polynomial coeﬃcients

1.17 AN INTRODUCTION TO DIFFERENTIAL GALOIS THEORY

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

1.19 Formal Solutions of Diﬀerential Equations

1.20 ON SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS WITH ALGEBRAIC SOLUTIONS

1.21 On second order homogeneous linear diﬀerential equations with Liouvillian solutions

1.22 Solutions of linear ordinary diﬀerential equations in terms of special functions

1.23 AN IMPLEMENTATION OF KOVACIC’S ALGORITHM FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS IN FORMAC

1.24 Algorithm implementation in FriCAS

1.25 Maxima implementation of Kovacic algorithm

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 MICHAEL F. SINGER. North Carolina State University. J. Symbolic Computation (1991) 11, 251-273.

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.

By Tolga Birkandan. arXiv:2010.01563v2, 28 June 2021.

By BRUCE SIMON. San Francisco State University. December 17, 2015.

By M. van Hoeij and J.A. Weil. Florida State University and Universit´e de Limoges. ISSAC’05, July 24–27, 2005, Beijing, China.

By MICHAEL F. SINGER. North Carolina State University. ISSAC ’89, Portland, Oregon, July 17, 1989.

By F. BALDASSARRI and B. DWORK. American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76

By Winfried Fakler. Vniversitiit Karlsruhe. Karlsruhe, Germany. Elsevier Science. Theoretical Computer Science 187 (1997) 2748.

By Manuel Bronstein and Sebastien Lafaille. INRIA – Projet. Proceedings of ISSAC’2002, Lille, ACM Press, 23-28

By A.Yu.Zherkov. Saratov State University, Saratov, USSR. 1987

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

By Nijso Beishuizen.

See https://sourceforge.net/p/maxima/mailman/message/32164642/