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

Dreyfus, Thomas

doi:10.1090/S0002-9939-2014-11826-0

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

Proc. Amer. Math. Soc. 142 (2014), 1193-1207

DOI: https://doi.org/10.1090/S0002-9939-2014-11826-0

Published electronically: January 24, 2014

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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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