Abstract:This paper is devoted to a complete parametric study of Liouvillian solutions of the general trace-free second order differential equation with a Laurent polynomial coefficient. This family of equations, for fixed orders at 0 and $$\infty$$
∞
of the Laurent polynomial, is seen as an affine algebraic variety. We prove that the set of Picard-Vessiot integrable differential equations in the family is an enumerable union of algebraic subvarieties. We compute explicitly the algebraic … Show more
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