  In this second paper on the method of deriving linearizing transformations
for nonlinear ODEs, we extend the method to a set of two coupled second order
nonlinear ODEs. We show that besides the conventional point, Sundman and
generalized linearizing transformations one can also find a large class of
mixed or hybrid type linearizing transformations like point-Sundman,
point-generalized linearizing transformation and Sundman-generalized
linearizing transformation in coupled second order ODEs using the integrals of
motion. We propose suitable algorithms to identify all these transformations
(with maximal in number) in a straightforward manner. We illustrate the method
of deriving each one of the linearizing transformations with a suitable
example.
