Solving second order equations by extending the PS method

Details Solving second order equations by extending the PS method Solving second order equations by extending the PS method

2000-01-03

arxiv.org/abs/math-ph/0001004v1

Journal of Physics A. Mathematical and General, Inglaterra, v. 34, 2001.

Physics

Mathematical Physics

10 pages

Scientific paper

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'.

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