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

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.

14 pages, final version. To appear in Proceedings of the American Mathematical Society

References in corpus (1)

• Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups

Cited by in corpus (6)

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• Difference algebraic relations among solutions of linear differential equations
• Computation of the unipotent radical of the differential Galois group for a parameterized second-order linear differential equation
• Calculating Galois groups of third order linear differential equations with parameters