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Characterisation of the algebraic properties of first integrals of scalar ordinary differential equations of maximal symmetry. (English) Zbl 0879.34052
Summary: We study the first integrals of linear nth order scalar ordinary differential equations with maximal symmetry. We establish patterns for the first integrals associated with these equations. It is shown that second and third order equations are the pathological cases in the study of higher order differential equations. The equivalence of contact symmetries for third order equations to non-Cartan symmetries of second order equations is highlighted.
MSC:
34C99Qualitative theory of solutions of ODE
37C80Symmetries, equivariant dynamical systems