NDLI: On Liouvillian solutions of linear differential equations of order 4 and 5

Content Provider	ACM Digital Library
Author	Cormier, Olivier
Abstract	In this paper we give the minimal possible degrees of an algebraic solution of the Riccati equation associated to an irreducible linear homogeneous differential equation of order 4 and 5, following the method used for the order 3 ([14]). We show that the algebraic degree of such a solution is bounded by 120 for the order 4 and by 55 for the order 5. With the important work done by Hessinger in [5] and the Tables computed in the sequel this leads to an algorithm to find Galois group and liouvillian solutions of equations of order 4.In the last section we construct an irreducible differential equation of degree 4 having SL(2, 7) as a Galois group and compute its liouvillian solutions. We also give the minimal polynomial over Q(x) of the algebraic solutions of the differential equation. This example illustrates a method which is easy to use in order to compute a liouvillian solution with the help of the Tables computed in this paper.
Starting Page	93
Ending Page	100
Page Count	8
File Format	PDF
ISBN	1581134177
DOI	10.1145/384101.384115
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2001-07-01
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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On Liouvillian solutions of linear differential equations of order 4 and 5