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We study differential equations $F(y,...,y^{\left(n\right)})=0$ where $F$ is a formal series in $y,y^{\prime },...,y^{\left(n\right)}$ with coefficients in some field of ${𝕂}_r$ with finite rank $r\in {\mathbb{N}}^{*}$. Our purpose is to express the support $\mathrm{Supp}{y}_0$, i.e. the set of exponents, of the elements $y_0\in {𝕂}_r$ that are solutions, in terms of the supports of the coefficients of the equation, namely $\mathrm{Supp}F$.