Computing integrability conditions for a cubic differential system. (English) Zbl 0871.34003
Summary: The integrability conditions for certain systems of differential equations \(\dot x=P(x,y)\), \(\dot y=Q(x,y)\), where \(P\) and \(Q\) are cubic polynomials, are obtained using two distinct computational approaches. Such conditions are required in the investigation of Hilbert’s 16th problem and in the development of algorithms for the automatic solution of differential equations.
MSC:
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
Keywords:
integrability conditions; differential equations; Hilbert’s 16th problem; automatic solution of differential equationsReferences:
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