Splitting differential equations using Galois theory
In some cases, solutions to a system of differential equations can be considered as a subset of the constants of some differentially closed field of characteristic zero together with some fixed solutions. When this happens, we say the set of generic solutions is internal to the constants of a differentially closed field of characteristic zero. In some cases, the pullback under the logarithmic derivative of algebraic ordinary differential equation which is almost internal to the constants is again internal. In joint work with Léo Jimenez we use model-theoretic Galois theory to develop a connection between the internality of a pullback and splitting of a short exact sequence of Galois groups.