Geodesic
Symmetry analysis of differential equations using MATHLIE
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 208-230

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This article discusses a general procedure to solve ordinary differential equations of arbitrary order. The method used is based on symmetries of differential equation. The known symmetries allow the derivation of first integrals of the equation. The knowledge of at least $r$ symmetries of an ordinary differential equation of order $n$ with $r\ge n$ is the basis for deriving the solution. Our aim is to show that Lie's theory is instrumental for solving an ordinary differential equation of higher-order. 
@article{ZNSL_1999_258_a10,
     author = {G. Baumann},
     title = {Symmetry analysis of differential equations using {MATHLIE}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {208--230},
     publisher = {mathdoc},
     volume = {258},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a10/}
}
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G. Baumann. Symmetry analysis of differential equations using MATHLIE. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 208-230. http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a10/