FCDiffEqSolve[mat, var, eps, n] constructs a solution for a single-variable differential equation G' = \varepsilon \mathcal{B} G in the canonical form, where mat is B, var is the variable w.r.t. which G was differentiated and n is the required order in eps.
The output consists of iterated integrals written in terms of FCIteratedIntegral objects.
Overview, FCIteratedIntegral, FCDiffEqChangeVariables
mat = {{-2/x, 0, 0}, {0, 0, 0}, {-x^(-1), 3/x, -2/x}}\left( \begin{array}{ccc} -\frac{2}{x} & 0 & 0 \\ 0 & 0 & 0 \\ -\frac{1}{x} & \frac{3}{x} & -\frac{2}{x} \\ \end{array} \right)
FCDiffEqSolve[mat, x, ep, 1]\left\{\text{ep} \left(C[1,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x,0,x\right)+C[1,1]\right)+C[1,0],\text{ep} C[2,1]+C[2,0],\text{ep} \left(C[3,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -2 \\ \end{array} \right),x\right),x,0,x\right)+C[1,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & -1 \\ \end{array} \right),x\right),x,0,x\right)+C[2,0] \;\text{FCIteratedIntegral}\left(\text{FCPartialFractionForm}\left(0,\left( \begin{array}{cc} \{x,-1\} & 3 \\ \end{array} \right),x\right),x,0,x\right)+C[3,1]\right)+C[3,0]\right\}