  Let L be a linear differential operator with coefficients in some
differential field k of characteristic zero with algebraically closed field of
constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we
determine the linear differential operator of minimal degree M and coefficients
in k^a, such that My=0. This result is then applied to some Picard-Fuchs
equations which appear in the study of perturbations of plane polynomial vector
fields of Lotka-Volterra type.
