  Linear time-invariant (LTI) systems appear frequently in natural sciences and
engineering contexts. Many LTI systems are described by ordinary differential
equations (ODEs). For example, biological gene regulation, analog filter
circuits, and simple mechanical, electrical, and hydraulic systems can all be
described with varying approximations as LTI systems using ODEs. While
linearity and time-invariance are straightforward to demonstrate for
closed-form system definitions, determining whether an ODE describes a system
with LTI properties is less obvious and rarely discussed in depth in the
literature. Complications arise due to slightly different definitions of
linearity in different contexts. This commentary is intended to provide clarity
on this subtle point, and act as an instructional aid or educational
supplement.
