On Singular Points Of Quasilinear Differential And Differential-Algebraic Equations

. We show how certain singularities of quasilinear differential and differentialalgberaic equations can be resolved by taking the solutions to be integral manifolds of certain distributions rather than curves with specific parametrization. 1. Introduction Recently there has been some interest in singularities of quasilinear differential and differential-algebraic equations, [3], [4], [9], [10], [11], [12], [13], [17]. We show that generalizing slightly the notion of solution regularizes certain singularities of these systems. The idea is to consider the solution curve geometrically as one-dimensional integral manifold of certain distribution without fixing any parametrization of it. In this way we are able to show that there are smooth solutions through certain points (in particular impasse points) which were previously considered as singular points. Some of the ideas of this article are implicit in [10], [11] and [17]. In [10] and [11] the given system with certain singularities is `..