On some algebraic differential equations with admissible algebroid solutions (Q1076866)

The differential equation with meromorphic coefficients \[ (1)\quad \sum_{\lambda \in I}c_{\lambda}w^{i_ 0}...(w^{(n)})^{i_ n}=\sum^{p}_{j=0}a_ jw^ j\quad /\sum^{q}_{k=0}b_ kw^ k \] where I is a finite set of multi-indices \(\lambda =(i_ 0,i_ 1,...,i_ n)\), \(i_ e\geq 0\) is studied. Under the assumption that (1) admits an admissible algebroid solution w with \(\nu\) branches the relations between \(\lambda\),p,q, and \(\nu\) are given.