Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Group Classification of a family of second-order differential equations   We find the group of equivalence transformations for equations of the form
$y''= A(x)y' + F(y),$ where $A$ and $F$ are arbitrary functions. We then give a
complete group classification of these families of equations, using a direct
method of analysis, together with the equivalence transformations.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: nlin
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol