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arXiv · 1110.1053

Computing the Galois group of some parameterized linear differential equation of order two

Thomas Dreyfus
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Abstract

We extend Kovacic's algorithm to compute the differential Galois group of some second order parameterized linear differential equation. In the case where no Liouvillian solutions could be found, we give a necessary and sufficient condition for the integrability of the system. We give various examples of computation.

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Thomas Dreyfus. 2011-10-05. Computing the Galois group of some parameterized linear differential equation of order two. https://doi.org/10.1090/s0002-9939-2014-11826-0

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