Abstract
Consider a second-order differential equation of the form y″ + ay ′ + by = 0 with a, b ϵ Q( x). Kovacic's algorithm tries to compute a solution of the associated Riccati equation that is algebraic and of minimal degree over Q̄ ( x). The coefficients of the monic irreducible polynomial of this solution are in C( x), where C is a finite algebraic extension of Q. In this paper we give a bound for the degree of the extension C ⊃ Q. Similar results are obtained for third-order differential equations.
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