Chrastina, Jan On formal theory of differential equations. II. (English) Zbl 0703.34001 Čas. Pěstování Mat. 114, No. 1, 60-105 (1989); corrections ibid. 114, No. 4, 411 (1989). [For part I see ibid. 111, 353-383 (1986; Zbl 0638.35008).] The main object of investigation is so-called diffieties which represent the infinite prolongations of general systems of PDE. The correspondence between ODE and diffieties is studied and the aim is to solve underdetermined systems of ODE (the number of unknown functions exceeds the number of equations). With the help of diffieties the original system of m-1 ODE for m unknown functions is replaced by its infinite prolongation and the Monge problem is reduced to the problem of the equivalence of Pfaffian systems. Reviewer: Y.V.Rogovchenko Cited in 1 ReviewCited in 1 Document MSC: 34A05 Explicit solutions, first integrals of ordinary differential equations 58A15 Exterior differential systems (Cartan theory) 58A17 Pfaffian systems Keywords:diffieties; Monge problem; Pfaffian systems Citations:Zbl 0638.35008 PDF BibTeX XML Cite \textit{J. Chrastina}, Čas. Pěstování Mat. 114, No. 1, 60--105 (1989; Zbl 0703.34001) Full Text: EuDML OpenURL