Solving second order equations by extending the PS method
L. G. S. Duarte, L. A. da Mota, J. E. F. Skea
Abstract
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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