solve linear system with non-constant coefficientss

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I would like to solve a linear system of two differential equations with non-constant coefficients. Namely a system of the form $$\begin{pmatrix}u_1 \\ u_2\end{pmatrix}'=A\begin{pmatrix}u_1 \\ u_2\end{pmatrix}$$

where $A=\begin{pmatrix}a &b\\ c& d\end{pmatrix}$ and $a,b,c,d$ are given holomorphic functions.

I'm mainly interested in integrate such a system along paths