  This paper is a sequel of our previous work in which we introduced the MapDE
algorithm to determine the existence of analytic invertible mappings of an
input (source) differential polynomial system (DPS) to a specific target DPS,
and sometimes by heuristic integration an explicit form of the mapping. A
particular feature was to exploit the Lie symmetry invariance algebra of the
source, without integrating its equations, to facilitate MapDE, making
algorithmic an approach initiated by Bluman and Kumei. In applications,
however, the explicit form of a target DPS is not available, and a more
important question is, can the source be mapped to a more tractable class. This
aspect was illustrated by giving an algorithm to determine the existence of a
mapping of a linear differential equation to the class of constant coefficient
linear differential equations, again algorithmically realizing a method of
Bluman and Kumei. Key for this application was the exploitation of a
commutative sub-algebra of symmetries corresponding to translations of the
independent variables in the target. In this paper, we extend MapDE to
determine if a source nonlinear DPS can be mapped to a linear differential
system. The methods combine aspects of the Bluman-Kumei mapping approach,
together with techniques introduced by Lyakhov et al,for the determination of
exact linearizations of ODE. The Bluman-Kumei approach which is applied to PDE,
focuses on the fact that such linearizable systems must admit an infinite Lie
subpseudogroup corresponding to the linear superposition of solutions in the
target. In contrast, Lyakhov et al., focus on ODE, and properties of the
so-called derived sub-algebra of the (finite) dimensional Lie algebra of
symmetries of the ODE. We also illustrate the powerful maximal symmetry groups
facility as a natural tool to be used in conjunction with MapDE.
