Abstract
In this paper we show how group theoretic information can be used to derive a set of necessary conditions on the coefficients ofL(y) forL(y=0 to have a liouvillian solution. The method is used to derive (and improve in one case) the necessary conditions of the Kovacic algorithm and to derive an explicit set of necessary conditions for third order differential equations.
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A weaker version of these results were announced inLiouvillian Solutions of Third Order Linear Differential Equations; New Bounds and Necessary Conditions, Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, ACM Press
Partially supported by NSF Grant 90-24624
Partially supported by Deutsche Forschungsgemeinschaft, while on leave from Universität Karlsruhe. This paper was written during the two year visit of the second author at North Carolina State University. The second author would like to thank North Carolina State University for its hospitality and support during the preparation of this paper
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Singer, M.F., Ulmer, F. Necessary conditions for liouvillian solutions of (third order) linear differential equations. AAECC 6, 1–22 (1995). https://doi.org/10.1007/BF01270928
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DOI: https://doi.org/10.1007/BF01270928