For a given second-order ordinary differential equation (ODE), several relationships among
first integrals, integrating factors and λ-symmetries are studied. The knowledge of a λ …

This paper studies relationships between the order reductions of ordinary differential
equations derived by the existence of λ-symmetries, telescopic vector fields and some …

We characterize the equations in the class A of the second-order ordinary differential
equations ẍ= M (t, x, ẋ) which have first integrals of the form A (t, x) ẋ+ B (t, x). We give an …

It is investigated how two (standard or generalized)-symmetries of a given second-order
ordinary differential equation can be used to solve the equation by quadratures. The method …

In this work, we establish a connection between the extended Prelle–Singer procedure with
five other analytical methods which are widely used to identify integrable systems in the …

TWISTED SYMMETRIES OF DIFFERENTIAL EQUATIONS Page 1 Article Journal of Nonlinear
Mathematical Physics, Vol. 16, Suppl. (2009) 107–136 c G. Gaeta TWISTED SYMMETRIES …

We consider a deformation of the prolongation operation, defined on sets of vector fields and
involving a mutual interaction in the definition of prolonged ones. This maintains …

We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our
results show that all the equations in Riccati chain share the same form of nonlocal …

We study the class of the ordinary differential equations of the form ẍ+ a2 (t, x) ẋ2+ a1 (t, x)
ẋ+ a0 (t, x)= 0, that admit v=∂ x as λ-symmetry for some λ= α (t, x) ẋ+ β (t, x). This class …

Here we discuss first integrals of a particular representation associated with second-order
ordinary differential equations. The linearization problem is a particular case of the …