  A criterion in the spirit of Rosenlicht is given, on the rational function
f(x), for when the planar vector field defined by x'=f(x) and y'=xy admits a
pair of algebraically independent first integrals over some extension of the
base field. This proceeds from model-theoretic considerations by working in the
theory of differentially closed fields of characteristic zero and asking: If D
is a strongly minimal set on the affine line that is internal to the constants,
when is the pullback of D under the logarithmic derivative itself internal to
the constants?
