Geodesic
On a cross system of two differential equations
Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 79-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article deals with the cross-system of the two differential equations of the second degree and fourth-degree derivative of the variables. The necessary and sufficient conditions for the Painlevé property for solutions of the system are found.
Keywords: system of the differential equations, property of Painleve, simplified differential equation. 
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I. P. Martynov; O. N. Parmanchuk; V. M. Pecevich. On a cross system of two differential equations. Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 79-83. http://geodesic.mathdoc.fr/item/PFMT_2013_3_a12/

[1] O. N. Parmanchuk, “Analiticheskie svoistva reshenii odnoi perekrestnoi sistemy dvukh differentsialnykh uravnenii”, Vestnik GrGU. Ser. 2. Matematika, fizika, informatika, vychislitelnaya tekhnika i upravlenie, biologiya, 2011, no. 2, 35–41

[2] N. S. Berezkina, I. P. Martynov, V. A. Pronko, “O sisteme dvukh drobno-lineinykh differentsialnykh uravnenii stepeni $n$ so svoistvom Penleve”, Differents. uravneniya, 42:4 (2006), 1–6 | MR

[3] C. Cosgrove, G. Scoufis, “Painleve classification of a class of differential equations of the second order and second degree”, Stud. Appl. Math., 88 (1993), 25–87 | MR | Zbl

[4] E. L. Ains, Obyknovennye differentsialnye uravneniya, GNTI, Kharkov, 1939, 719 pp.

[5] F. Bureau, “Differential equations with fixed critical points”, Ann. di Math. Sci., 64 (1964), 229–364 | DOI | MR | Zbl