Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Euler-Imshenetsky-Darboux transformation of second-order linear
  differential equations   It is shown, how to generate infinite sequences of differential equations of
the second order based on some standard equations, using
Euler-Imshenetsky-Darboux (EID) transformation. For all this, factorizations of
differential operators and operational identities are used.Some generalizations
of integrable cases of Schr\"odinger's equations are finded. The example of
integrable equation with liouvillian coefficients, that, apparently, can not be
solved by Singer and Kovacic's algorithm (and its modifications), was built.
The alogorithm and the program for solving conctructed classes of equations,
was realized in REDUCE system. Corresponding procedure GENERATE is addendum to
the ODESOLVE procedure of REDUCE system. The results of using GENERATE
procedure (REDUCE 3.8) was compared with results of DSolve procedure (Maple
10). Though, algorithm, based on EID transformation is not an alternative to
the unviersal ones, in the borders of its applicability, its very powerful.

37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph