I need to know how to solve this complicated differential equation in $z$ either analytically or numerically :
\begin{eqnarray} \frac{dx_1}{dz} &=& -ib_1x_1 - ikx_2 \\ \frac{dx_2}{dz} &=& -i(b_2+c_2\cos(d_2z))x_2-ikx_1 \end{eqnarray}
where $b_1$, $b_2$, $c_2$, $d_2$, $k$ are constants, $i^2 = -1$ and initial condition $x_1(0)$, $x_2(0)$ are known also range of $z$.