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Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations

✍ Scribed by Michael F. Singer


Book ID
115512555
Publisher
John Hopkins University Press
Year
1981
Tongue
English
Weight
34 KB
Volume
103
Category
Article
ISSN
0002-9327

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The Kovacic algorithm and its improvements give explicit formulae for the Liouvillian solutions of second order linear differential equations. Algorithms for third order differential equations also exist, but the tools they use are more sophisticated and the computations more involved. In this paper

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Singer and Ulmer (1997) gave an algorithm to compute Liouvillian ("closed-form") solutions of homogeneous linear differential equations. However, there were several efficiency problems that made computations often not practical. In this paper we address these problems. We extend the algorithm in