Geodesic
Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method
Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 75-91

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The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular, we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries) into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form of the Lie system is found explicitly. 
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     author = {Yu. R. Romanovskii},
     title = {Computation of local symmetries of second-order ordinary differential equations by the {Cartan} equivalence method},
     journal = {Matemati\v{c}eskie zametki},
     pages = {75--91},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a7/}
}
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Yu. R. Romanovskii. Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method. Matematičeskie zametki, Tome 60 (1996) no. 1, pp. 75-91. http://geodesic.mathdoc.fr/item/MZM_1996_60_1_a7/