Method of Frobenius for a matrix differential equation?

Question

Suppose we have the following matrix differential equation, $$\textbf{Y}'(x)=\frac{1}{x}\textbf{A}(x)\textbf{Y}(x),$$ where $$\textbf{Y}(x) = [y_1(x), y_2(x), ..., y_m(x)]^T$$ is a vector and $$\textbf{A}(x)=[a_{ij}(x)]_{1\le i,j,\le m},$$ is a matrix which is smooth and analytic at $x=0$. Are we able to solve this using the method of Frobenius? Can we generate a series of the form $$\textbf{Y}(x)=x^\sigma\sum_{n=0}^\infty\textbf{Y}_n x^n,$$ where $\sigma$ is given by some kind of indicial equation (see Wikiepdia on the Frobenius method)?. Do you know how to calculate a recurrence relation? I want something similar to that shown in this document. They calculate a power series solution which only works if $A(x)/x$ is analytic at $x=0$.