Particular integrals of systems in total differentials. (Russian) Zbl 0760.34004

Gorbuzov, V. N.; Tyshchenko, V. Yu.

Differ. Uravn. 27, No. 10, 1819-1822 (1991).

Conditions for existence of particular integrals for systems of the form \[ dx_ i=\sum^ m_{j=1}P_{ij}(x_ 1,\dots,x_ n,t_ 1,\dots,t_ m)dt_ j,\quad i=1,2,\dots,n \] are given, where \(P_{ij}\) are polynomials in \(x_ i\) with coefficients analytic in \(t_ j\).

Reviewer: B.Maslowski

MSC:

34A05

Explicit solutions, first integrals of ordinary differential equations

Keywords:

systems in total differentials; existence of particular integrals