Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solving second order equations by extending the PS method   An extension of the ideas of the Prelle-Singer procedure to second order
differential equations is proposed. As in the original PS procedure, this
version of our method deals with differential equations of the form
y''={M(x,y,y')}/{N(x,y,y')}, where M and N are polynomials with coefficients in
the field of complex numbers C. The key to our approach is to focus not on the
final solution but on the first-order invariants of the equation. Our method is
an attempt to address algorithmically the solution of SOODEs whose first
integrals are elementary functions of x, y and y'.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph