On a set of Grassmann-valued extensions of systems of ordinary differential equations

Formulations of some Grassmann-valued systems of ordinary differential equations invariant under (infinitesimal) supersymmetry transformations, including $N$-superspace extended types, are reviewed and discussed, with use of superfields. Different new examples are shown, and some aspects on methods for obtaining solutions are offered. Notions inspired from Darboux theory are considered for some general polynomial systems, involving Grassmann variables.