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Rational first integrals for periodic systems
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Mathematics in Computer ScienceLet \(\mathbb{K}\) be a field of characteristic zero and let \(\mathbb{K}(x)\) be a differential field, equipped with a derivation \(\delta_x=d/dx\). Finding a rational first integral of an ordinary differential equation of the form \(dy/dx=p(x,y)\), where \(p(x,y)\in\mathbb{K}(x,y)\), is a central problem in the algebraic theory of ODEs that goes back
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