Abstract
Let F be an irreducible differential polynomial over k(t) with k being an algebraically closed field of characteristic zero. The authors prove that F = 0 has rational general solutions if and only if the differential algebraic function field over k(t) associated to F is generated over k(t) by constants, i.e., the variety defined by F descends to a variety over k. As a consequence, the authors prove that if F is of first order and has movable singularities then F has only finitely many rational solutions.
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