Abstract
We present a geometric exposition of S. Lie's and E. Cartan's theory of explicit integration of finite-type (in particular, ordinary) differential equations. Numerous examples of how this theory works are given. In one of these, we propose a method of hunting for particular solutions of partial differential equations via symmetry preserving overdetermination.
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Duzhin, S.V., Lychagin, V.V. Symmetries of distributions and quadrature of ordinary differential equations. Acta Appl Math 24, 29–57 (1991). https://doi.org/10.1007/BF00047361
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DOI: https://doi.org/10.1007/BF00047361