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 …

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 …

In this paper we give a Lax formulation for a family of non-autonomous second-order
differential equations of the type yz z+ a 3 (z, y) yz 3+ a 2 (z, y) yz 2+ a 1 (z, y) y z+ a 0 (z, y) …

Scalar second-order ordinary differential equations with cubic nonlinearity in the first-order
derivative are considered. Lie symmetries admitted by an arbitrary equation are described in …

In this paper,(1) We show that if there are not enough symmetries and λ-symmetries, some
first integrals can still be obtained. And we give two examples to illustrate this theorem.(2) …

We consider a family of non-autonomous second-order differential equations, which
generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions …

In Cauchy problems with blow-up solutions there exists a singular point whose position is
unknown a priori (for this reason, the application of standard fixed-step numerical methods …

Singularly perturbed boundary-value problems for second-order ODEs of the form ε
yxx′′= F (x, y, yx′) with ε→ 0 are considered. We present a new method of numerical …

For ordinary differential equations, the genesis of the concept of C https://s3-euw1-ap-pe-df-
pch-content-public-p. s3. eu-west-1. amazonaws. com/9780429263743/15e65f54-7536 …

In this paper, we provide some geometric properties of λ‐symmetries of ordinary differential
equations using vector fields and differential forms. According to the corresponding …