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Comparison of Noether Symmetries and First Integrals of Two-Dimensional Systems of Second Order Ordinary Differential Equations by Real and Complex Methods
Noether symmetries and first integrals of a class of two-dimensional systems of second order ordinary differential equations (ODEs) are investigated using real and complex methods. We show that first integrals of systems of two second order ODEs derived by the complex Noether approach cannot be obtained by the real methods. …