In this work we consider a family of cubic, with respect to the first derivative, second-order
ordinary differential equations. We study linearizability conditions for this family of equations …

The class of nonlinear second-order equations that are linearizable by means of
generalized Sundman transformations (S-transformations) is identified as the class of …

In this work we consider a family of nonlinear oscillators that is cubic with respect to the first
derivative. Particular members of this family of equations often appear in numerous …

Nonlinear second-order ordinary differential equations are common in various fields of
science, such as physics, mechanics and biology. Here we provide a new family of …

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 consider a family of nonlinear oscillators with quadratic damping, that generalizes the
Liénard equation. We show that certain nonlocal transformations preserve autonomous …

Using the coefficients of a system semilinear cubic in the first derivative second order
differential equations one defines a connection in the space of the independent and …

For Liénard I-type equations it is proved the existence of a family of λ− symmetries such that
any of them lets the computation by quadratures of a time-dependent first integral of the …

In the literature, the generalized Sundman transformation has been used for obtaining
necessary and sufficient conditions for a single second-and third-order ordinary differential …

We employ the method of nonlocal generalized Sundman transformations to formulate the
linearization problem for equations of the generalized Liénard type and show that they may …