  Lie's linearizability criteria for scalar second-order ordinary differential
equations had been extended to systems of second-order ordinary differential
equations by using geometric methods. These methods not only yield the
linearizing transformations but also the solutions of the nonlinear equations.
Here complex methods for a scalar ordinary differential equation are used for
linearizing systems of two second-order ordinary and partial differential
equations, which can use the power of the geometric method for writing the
solutions. Illustrative examples of mechanical systems including the Lane-Emden
type equations which have roots in the study of stellar structures are
presented and discussed.

Classical Analysis and ODEs