Kachevskij, D. N. On first integrals of a system of differential equations. (Russian) Zbl 0602.34008 Differ. Uravn. 20, No. 10, 1819-1821 (1984). This paper deals with systems of ordinary differential equations of the form \(\ddot q_ i=\alpha_ i(t,q_ 1,...,q_ n,\dot q_ 1,...,\dot q_ n),\) \(i=1,2,...,n\), in which the right-hand sides are twice continuously differentiable. Assuming that a differentiable function \(f(t,q_ 1,...,q_ n,\dot q_ 1,...,\dot q_ n)\) does exist, such that \(df/dt=\partial \alpha_ k/\partial q_ k,\) \(k=1,2,...,n\), then a first integral of the system can be constructed. Reviewer: C.Corduneanu MSC: 34A34 Nonlinear ordinary differential equations and systems Keywords:second order differential equation; first integral PDFBibTeX XMLCite \textit{D. N. Kachevskij}, Differ. Uravn. 20, No. 10, 1819--1821 (1984; Zbl 0602.34008)