Govinder, K. S.; Leach, P. G. L. Integrability of generalized Ermakov systems. (English) Zbl 0830.34002 J. Phys. A, Math. Gen. 27, No. 12, 4153-4156 (1994). Summary: We find all (four) first integrals for the two-dimensional Ermakov systems \[ \ddot x+ \omega^2(t) x= \textstyle{{1\over x^2}} f(y/x),\quad \ddot y+ \omega^2(t)y= \textstyle{{1\over y^3}} g(y/x). \] {}. Cited in 6 Documents MSC: 34A05 Explicit solutions, first integrals of ordinary differential equations 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. Keywords:integrability; first integrals; two-dimensional Ermakov PDFBibTeX XMLCite \textit{K. S. Govinder} and \textit{P. G. L. Leach}, J. Phys. A, Math. Gen. 27, No. 12, 4153--4156 (1994; Zbl 0830.34002) Full Text: DOI