  Multivariate Bessel processes describe Calogero-Moser-Sutherland particle
models and are related with $\beta$-Hermite and $\beta$-Laguerre ensembles.
They depend on a root system and a multiplicity $k$. Recently, several limit
theorems for $k\to\infty$ were derived where the limits depend on the solutions
of associated ODEs in these freezing regimes. In this paper we study the
solutions of these ODEs which are are singular on the boundaries of their
domains. In particular we prove that for a start in arbitrary boundary points,
the ODEs always admit unique solutions in their domains for $t>0$.
