Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analytic technique for the solutions of nonlinear oscillators with
  damping using the Abel Equation   Using the Chiellini condition for integrability we derive explicit solutions
for a generalized system of Riccati equations $\ddot{x}+\alpha
x^{2n+1}\dot{x}+x^{4n+3}=0$ by reduction to the first-order Abel equation
assuming the parameter $\alpha\ge 2\sqrt{2(n+1)}$. The technique, which was
proposed by Harko \textit{et al}, involves use of an auxiliary system of
first-order differential equations sharing a common solution with the Abel
equation. In the process analytical proofs of some of the conjectures made
earlier on the basis of numerical investigations in \cite{SJKB} is provided.

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The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg