Diaconescu, O. V. Multi-dimensional Darboux type differential systems with quadratic nonlinearities. (English) Zbl 1136.34035 Bul. Acad. Ştiinţe Repub. Mold., Mat. 2007, No. 1(53), 95-100 (2007). Algebraic and invariant approaches to differential equations provide criteria for reductions to simpler forms. In this essential work, the autonomous \(n\)-dimensional \((n>1)\) system of first-order ODEs with quadratic nonlinearities are studied under the action of the group of centre-affine transformations. If the first-order system under investigation admits an (\(n-1\))-dimensional abelian Lie algebra of operators, then an integrating factor gives rise to an integral of the system. As a consequence, for such systems, the authors construct \(\mathrm{GL}(n, \mathbb R)\)-integrals and first integrals of Darboux type. Reviewer: F. M. Mahomed (Johannesburg) MSC: 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 34C14 Symmetries, invariants of ordinary differential equations Keywords:invariant approach; Darboux systems; linear group PDFBibTeX XMLCite \textit{O. V. Diaconescu}, Bul. Acad. Științe Repub. Mold., Mat. 2007, No. 1(53), 95--100 (2007; Zbl 1136.34035)