Linearization criteria for a system of second-order ordinary differential equations

Conditional Linearizability of Fourth-Order Semi-Linear Ordinary Differential Equations

“…Its coefficients are given by (22) and come out to be c = −x/y 2 , g = 1/y, h = 2/x, d = 0. They satisfy the constraints (23) and linearizability criteria (9 …”

“…Though little progress was made (as discussed below) towards providing explicit procedures for linearizing systems of ODEs, it was shown [23] that there will generally be multiple classes, even for second-order systems.…”

Geometric Linearization of Ordinary Differential Equations

“…One may wonder if the extension provided for systems will give a unique class as well. The answer is "No", as it is known that for 2-dimensional systems there are five classes [4] that are linearizable and only one has been provided by the above procedure. How is it that the case of the single equation is fully covered by the above procedure but the systems are not fully covered?…”

“…He did not go further to deal with systems of ODEs or third order ODEs. His procedure uses transformations of the dependent and independent variables of the ODE (or system of ODEs) There has been work done on obtaining the symmetry classes of systems of second order ODEs [4] and for the third order ODE [5]. Some explicit criteria for the linearizability of single third order ODEs have also been provided in the literature [6,7,8,9,11,12].…”

Linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations

“…Linearization of deterministic ordinary differential equations (ODEs) has been studied by various authors (see for example [1,3,4,13]). Linearization criteria for one-dimensional Itô SODEs have been given by Gard [5].…”