Abstract
The largest group of Lie symmetries that a third-order ordinary differential equation (ode) may allow has seven parameters. Equations sharing this property belong to a single equivalence class with a canonical representative v ′′′(u)=0. Due to this simple canonical form, any equation belonging to this equivalence class may be identified in terms of certain constraints for its coefficients. Furthermore a set of equations for the transformation functions to canonical form may be set up for which large classes of solutions may be determined algorithmically. Based on these steps a solution algorithm is described for any equation with this symmetry type which resembles a similar scheme for second order equations with projective symmetry group.
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Received March 9, 2000; revised June 8, 2000
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Schwarz, F. Solving Third Order Differential Equations with Maximal Symmetry Group. Computing 65, 155–167 (2000). https://doi.org/10.1007/s006070070017
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DOI: https://doi.org/10.1007/s006070070017