  This study will explicitly demonstrate by example that an unrestricted
infinite and forward recursive hierarchy of differential equations must be
identified as an unclosed system of equations, despite the fact that to each
unknown function in the hierarchy there exists a corresponding determined
equation to which it can be bijectively mapped to. As a direct consequence, its
admitted set of symmetry transformations must be identified as a weaker set of
indeterminate equivalence transformations. The reason is that no unique general
solution can be constructed, not even in principle. Instead, infinitely many
disjoint and thus independent general solution manifolds exist. This is in
clear contrast to a closed system of differential equations that only allows
for a single and thus unique general solution manifold, which, by definition,
covers all possible particular solutions this system can admit. Herein,
different first order Riccati-ODEs serve as an example, but this analysis is
not restricted to them. All conclusions drawn in this study will translate to
any first order or higher order ODEs as well as to any PDEs.
