On 5-dimensional groups of pointwise symmetries of third-order ordinary differential equations

Abstract EN

In this paper the authors have studied the geometry of the third – order ordinary differential equations.

They have established a necessary and sufficient condition, for such equations to posses a five – dimensional group of pointwise symmetries.

Using the Cartan,s method of exterior forms, the structural equations have been obtained.

The authors have concluded that the transformations group g5,5 is a five – dimensional group for a third – order ordinary differential equation.