44 research outputs found
Group Classification of a family of second-order differential equations
We find the group of equivalence transformations for equations of the form
where and are arbitrary functions. We then give a
complete group classification of these families of equations, using a direct
method of analysis, together with the equivalence transformations.Comment: 13 page
Some variational principles associated with ODEs of maximal symmetry. Part 1: Equations in canonical form
Variational and divergence symmetries are studied in this paper for linear
equations of maximal symmetry in canonical form, and the associated first
integrals are given in explicit form. All the main results obtained are
formulated as theorems or conjectures for equations of a general order. Some of
these results apply to linear equations of a general form and of arbitrary
orders or having a symmetry algebra of arbitrary dimension