# Solution to matrix ODE $Ay'[x] + B\frac{y[x]}{x} + Cy[x] = 0$?

Does there exist a closed form solution to the homogeneous system of ODEs

$$Ay'[x] + B\frac{y[x]}{x} + Cy[x] = 0,$$

where $A$, $B$, and $C$ are $n$ x $n$ (constant) matrices, and $y$ is an $n$-vector of solutions (with $n > 1$ of course). For the specific case that I am interested in, $A$ is symmetric, $B$ is antisymmetric, and $C$ is diagonal; all three matrices are invertible.

-