  Below we study a linear differential equation $\MM
(v(z,\eta))=\eta^M{v(z,\eta)}$, where $\eta>0$ is a large spectral parameter
and $\MM=\sum_{k=1}^{M}\rho_{k}(z)\frac{d^k}{dz^k},\; M\ge 2$ is a differential
operator with polynomial coefficients such that the leading coefficient
$\rho_M(z)$ is a monic complex-valued polynomial with $\dgr{\rho_M }=M$ and
other $\rho_k(z)$'s are complex-valued polynomials with $\dgr{\rho_k }\leq k$.
We prove the Borel summability of its WKB-solutions in the Stokes regions. For
$M=3$ under the assumption that $\rho_M$ has simple zeros, we give the full
description of the Stokes complex (i.e. the union of all Stokes curves) of this
equation. Finally, we show that for the Euler-Cauchy equations, their
WKB-solutions converge in the usual sense.
