ON SOLUTIONS OF LINEAR ORDINARY DIFFERENTIAL-EQUATIONS IN THEIR COEFFICIENT FIELD

We describe a rational algorithm for finding the denominator of any solution of a linear ordinary differential equation in its coefficient field. As a consequence, there is now a rational algorithm for finding all such solutions when the coefficients can be built up from the rational functions by finitely many algebraic and primitive adjunctions. This also eliminates one of the computational bottlenecks in algorithms that either factor or search for Liouvillian solutions of such equations with Liouvillian coefficients. © 1992, Academic Press Limited. All rights reserved.