The Prelle-Singer method is a semi-decision procedure for solving nonlinear first-order ordinary differential equations of the form 
, where 
and 
are polynomials. It is based on knowledge of the structure
of the integrating factor, and requires the
specification of degree bounds for polynomials in the integrating factor. Duarte
et al. (2000) have extended the Prelle-Singer procedure to second-order ODEs
of the form 
,
again with 
and 
polynomials.
Prelle-Singer Method
This entry contributed by Bhuvanesh Bhatt
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References
Duarte, L. G. S.; da Mota, L. A.; and Skea, J. E. F. "Solving Second Order Ordinary Differential Equations by Extending the PS Method." 3 Jan 2000. http://arxiv.org/abs/math-ph/0001004.Man, Y. K. and MacCallum, M. A. H. "A Rational Approach to the Prelle-Singer Algorithm." J. Symb. Comput. 24, 31-43, 1997.Prelle, M. and Singer, M. "Elementary First Integrals of Differential Equations." Trans. Amer. Math. Soc. 279, 215-229, 1983.Singer, M. "Liouvillian First Integrals of Differential Equations." Trans. Amer. Math. Soc. 333, 673-688, 1992.Referenced on Wolfram|Alpha
Prelle-Singer MethodCite this as:
Bhatt, Bhuvanesh. "Prelle-Singer Method." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Prelle-SingerMethod.html