Title: Algorithmic Verification of Linearizability for Ordinary Differential Equations,
Abstract: For a nonlinear ordinary differential equation solved with respect to the
highest order derivative and rational in the other derivatives and in the
independent variable, we devise two algorithms to check if the equation can be
reduced to a linear one by a point transformation of the dependent and
independent variables. The first algorithm is based on a construction of the
Lie point symmetry algebra and on the computation of its derived algebra. The
second algorithm exploits the differential Thomas decomposition and allows not
only to test the linearizability, but also to generate a system of nonlinear
partial differential equations that determines the point transformation and the
coefficients of the linearized equation. Both algorithms have been implemented
in Maple and their application is illustrated using several examples.