infgen([xi, eta], k, y(x))

infgen([xi, eta], k, ODE)

infgen([xi, eta], k, y(x), ODE)

The infinitesimals xi and eta of the one-parameter rotation group and the first extension of the related infinitesimal generator

When an ODE is given as an argument, its right hand side is used to replace all occurrences of the highest derivative in the infinitesimal generator. To obtain a meaningful result, the ODE is invariant under the related symmetry group (or at least more general than the related invariant ODE). For example, this is the most general first order ODE invariant under rotations in the plane.

The first extension of the related infinitesimal generator is given by

It was not necessary to also give y(x) above, since this information is already present in the ODE.

The most general case of a point symmetry and the first extension of the related infinitesimal generator

The final example illustrates the most general case of a dynamical symmetry in the context of second order ODEs and the first extension of the related infinitesimal generator. When working with dynamical symmetries, the ODE itself is required as an argument.

DEtools, dsolve,Lie, eta_k, PDEtools, symgen