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Lie point symmetries for systems of second order linear ordinary differential equations. (English) Zbl 0649.34018
Recently it was shown that some nonlinear second order differential equations could be linearized by a point transformation generated by the generator $G=\tau \partial /\partial t+\eta \partial /\partial x,$ where $\tau =\tau \left(x,t\right)$, $\eta =\eta \left(x,t\right)$ are unknown coefficients. Because the set of all generators of a differential equation creates a Lie algebra under the operation of the Lie bracket it is interest in finding the number of generators for a system of differential equations. The paper in the heading deals with the mentioned problem for the system ${x}^{\text{'}\text{'}}=ax+by$, ${y}^{\text{'}\text{'}}=cx+dy$, where a,b,c,d are constant coefficients. Some considerations are extended to higher dimensional systems. The case when a,b,c,d depend upon t is also discussed.
Reviewer: J.Banás
##### MSC:
 34A30 Linear ODE and systems, general 22E60 Lie algebras of Lie groups 17B15 Representations of Lie algebras, analytic theory