Zernov, A. E. Existence and asymptotics of solutions of an implicit Cauchy problem with a singularity. (English. Russian original) Zbl 0810.34002 Differ. Equations 28, No. 12, 1808-1809 (1992); translation from Differ. Uravn. 28, No. 12, 2168-2169 (1992). The author considers an implicit Cauchy problem of the type \[ tx'= ax^ 2+ bt+ f(t,x,x'),\quad x(0)= 0. \] He obtains sufficient conditions for the existence of continuously differentiable solutions with prescribed asymptotic properties. Reviewer: W.Müller (Berlin) MSC: 34A09 Implicit ordinary differential equations, differential-algebraic equations 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:implicit Cauchy problem; continuously differentiable solutions; prescribed asymptotic properties PDFBibTeX XMLCite \textit{A. E. Zernov}, Differ. Equations 28, No. 12, 2168--2169 (1992; Zbl 0810.34002); translation from Differ. Uravn. 28, No. 12, 2168--2169 (1992)