How to define singular solutions
Because implicit first order differential equations may have two- parameter families of solutions, the notions of ``general solution'' and ``singular solution'' as sometimes described in elementary texts are not appropriate. The authors use the ideas of contact geometry to give rigorous definitions, improving on an earlier approach by \textit{M. T. Fukuda} [Yokohama Math. J. 25, 41-58 (1977; Zbl 0372.34026)]. The approach is elementary and the main results can be extended to partial differential equations.
implicit first order differential equations
scientific article; zbMATH DE number 515594