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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
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