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Laguerre E., Sur quelques invariants des équations différentielles linéaires. C.R. Acad. Sci. Paris, 88 (1879) 224–227.
LIE S., Klassifikation and Integration von gewöhnlichen Diferentialgleichungen zwischen x, y, die eine Gruppe von Transformationen gestatten. I to IV. Arch. for Math Kristiana 1883–1884, new edition for I, II in Math. Ann. 1888–1889. The four papers are reproduced in Sophus Lie Gesammelte Abhandlungen, vol 5, X, XI, XIV, XVI. Teubner (Leipzig 1924).
OVSIANNIKOV L.V., Group analysis of differential equations (translation from Russian). Academic Press, 1982.
IBRAGIMOV N.H., Transformation groups applied to mathematical physics (translation from Russian). Reidel 1985.
OLVER P.J., Applications of Lie groups to differential equations. Springer, 1986.
LIE S., Vorlesungen fiber continuierliche Gruppen mit geometrischen and anderen Anwendungen. Bearbeitet and herausgegeben von Dr G. Scheffers, Teubner (Leipzig 1893), Chap. 12, p. 298, “Satz 3”.
LIE S., Theorie der Transformations gruppen, dritter abschnitt, Abtheilung I, Unter Mitwirkung von Pr. Dr F. Engel, Teubner (Leipzig 1893).
Krause J., Michel L., Equations differentielles linéaires d'ordre n > 2 ayant fine algébre de Lie de symétrie de dimension n + 4, C.R. Acad. Sci. Paris, 307 (1988) 905–910.
MAHOMED P.M., LEACH P.G.L., Symmetry Lie algebras of nth order ordinary differential equations, to appear in J. Math. Anal. Appl. (Preprint Dept. Computational and Applied Mathematics, Univ. of the Witwatersrand, Johannesburg, S.A.)
TRESSE A.,Détermination des invariants ponctuels de l'équation différentielle ordinaire du second ordre y” = ω(χ) y, y'). Gekrönte Preisschrift, Hirzel, Leipzig 1896.
Arnold V., Chapitres supplementaires de la théorie des equations différentielles ordinaires. I6E exercice, Nauka, Moscou 1978.
research is supported by FONDECYT (project 0462/89). L.M. has benefited from it; he is also grateful to DIUC, Pontificia Universidad Católica de Chile, for an invitation in the fall of 1989.
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Krause, J., Michel, L. (1991). Classification of the symmetries of ordinary differential equations. In: Dodonov, V.V., Man'ko, V.I. (eds) Group Theoretical Methods in Physics. Lecture Notes in Physics, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54040-7_116
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DOI: https://doi.org/10.1007/3-540-54040-7_116
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