  We study differential equations $F(y,...,y^{(n)})=0$ where $F(Y_0,...,Y_n)$
is a formal series in $Y_0,...,Y_n$ with coefficients in some field of
\emph{generalized power series} $\mathds{K}_r$ with finite rank
$r\in\mathbb{N}^*$. Our purpose is to understand the connection between the set
of exponents of the coefficients of the equation $\textrm{Supp} F$ and the set
$\textrm{Supp} y_0$ of exponents of the elements $y_0\in\mathds{K}_r$ that are
solutions.
