Generalized Whittaker's equations for holonomic mechanical systems.
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International Journal of Mathematics and Mathematical Sciences
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Hussain, Munawar (1978)
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We study integrability of two-dimensional autonomous systems in the plane with center type linear part. For quadratic and homogeneous cubic systems we give a simple characterization for integrable cases, and we find explicitly all first integrals for these cases. Finally, two large integrable system classes are determined in the most general nonhomogeneous cases.