  We discuss the effective computation of geometric singularities of implicit
ordinary differential equations over the real numbers using methods from logic.
Via the Vessiot theory of differential equations, geometric singularities can
be characterised as points where the behaviour of a certain linear system of
equations changes. These points can be discovered using a specifically adapted
parametric generalisation of Gaussian elimination combined with heuristic
simplification techniques and real quantifier elimination methods. We
demonstrate the relevance and applicability of our approach with computational
experiments using a prototypical implementation in Reduce.
