  In this article, we consider a higher-order elliptic equation with nonsmooth
coefficients with respect to Orlicz spaces on the domain
$\Omega\subset\mathbb{R}^{n}$. The separable subspace of this space is
distinguished in which infinitely differentiable and compactly supported
functions are dense; Sobolev spaces generated by these subspaces are
determined. We demonstrate the local solvability of the equation in
Orlicz-Sobolev spaces under specific restrictions on the coefficients of the
equation and the Boyd indices of the Orlicz space. This result strengthens the
previously known classical $L_{p}$ analog.
