The central and secondary link problems for an equation and a second rank system

For the equation
\begin{equation} \sum_{\nu=0}^{n}P_\nu(z)y^{(\nu)}=0, \quad P_\nu(z)=a_{\nu0}+a_{\nu1}z, \quad P_n(z)=1, \tag{1} \end{equation}
($a_{\nu0}$, $a_{\nu1}$ are parameters) and the system of $n$ equations
\begin{equation} \bar{y}^{(1)}=(A_0+A_1z)\bar{y}, \quad A_1=\operatorname{diag}\{0,\dots,0,\lambda\}. \tag{2} \end{equation}
($A_0$, $A_1$ are constant matrices), fundamental matrices $\Phi(z)$ and $\Phi^*(z)$ are constructed each of which has an asymptotic expansion in parabolic cylinder functions as well as an asymptotic expansion in powers of $1/z$ in open halfplanes. The following results are obtained: a) the constant matrix appearing in the relation $\Phi(z)=\Phi^*(z)F$ is found (the secondary problem); b) expansions of $\Phi(z)$ and $\Phi^*(z)$ in series in powers of $z$ are established (the central problem).