The results presented in this paper are unbelievably trivial. This
sad fact is disguised by the misleading title and by an extensive
redundant blabla. In essence, elementary expressions (4.20), (4.24)
and (4.25) are shown to satisfy differential eq. (1.3) with suitable
coefficients. The only explanation why this paper could have been
accepted for publication in J. Phys. A can be seen in the absolute
professional incompetency of its referees. Interested readers should
return to ref. [11] (containing basically the same message plus much 
much more, and
published as early as in 1978!) or glimpse in the comprehensive
monograph ``Quasi-exactly solvable models in quantum mechanics'' by
Alexander G. Ushveridze (IOP, 1994). There also exists a truly
extensive and exciting further reading on the subject - the current
reviewer is prepared to provide its (incomplete) list (involving
names like A. Hautot or A. Turbiner or C. M. Bender, etc) upon
request.




MR2812321 Hu, Juan; Yu, Guo-Fu The application of value distribution
theory to a doubly anharmonic oscillator. J. Phys. A 44 (2011), no.
29, 295205, 7 pp. 81Qxx