  This article is interested in pullbacks under the logarithmic derivative of
algebraic ordinary differential equations. In particular, assuming the solution
set of an equation is internal to the constants, we would like to determine
when its pullback is itself internal to the constants. To do so, we develop,
using model-theoretic Galois theory and differential algebra, a connection
between internality of the pullback and the splitting of a short exact sequence
of algebraic Galois groups. We then use algebraic group theory to obtain
internality and non-internality results.
