  We study general (not necessarily Hamiltonian) first-order symmetric systems
$J y'(t)-B(t)y(t)=\D(t) f(t)$ on an interval $[a,b> $ with the regular endpoint
$a$. The deficiency indices $n_\pm$ of the corresponding minimal relation
$\Tmi$ may be arbitrary (possibly unequal). Our approach is based on the
concept of a decomposing boundary triplet, which enables one to parametrize
various classes of extensions of $\Tmi$ (self-adjoint, $m$-dissipative, etc.)
in terms of boundary conditions imposed on regular and singular values of a
function $y\in \dom \tma$ at the endpoints $a$ and $b$ respectively. In
particular, we describe self-adjoint and $\l$-depending Nevanlinna boundary
conditions which are analogs of separated ones for Hamiltonian systems. With a
boundary value problem involving such conditions we associate the $m$-function
$m(\cd)$, which is an analog of the Titchmarsh-Weyl coefficient for the
Hamiltonian system. In the simplest case of minimal (unequal) deficiency
indices $n_\pm$ the $m$-function $m(\cd)$ coincides with the rectangular
Titchmarsh-Weyl coefficient introduced by Hinton and Schneider. We parametrize
all $m$-functions in terms of the Nevanlinna boundary parameter at the endpoint
$b$ by means of the formula similar to the known Krein formula for resolvents.
Application of these results to differential operators of an odd order enables
us to complete the results by Everitt and Krishna Kumar on the Titchmarsh-Weyl
theory of such operators.
