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Rational Solutions of Abel Differential Equations

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 نشر من قبل Luis \\'Angel Calder\\'on P\\'erez
 تاريخ النشر 2021
  مجال البحث
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We study the rational solutions of the Abel equation $x=A(t)x^3+B(t)x^2$ where $A,Bin C[t]$. We prove that if $deg(A)$ is even or $deg(B)>(deg(A)-1)/2$ then the equation has at most two rational solutions. For any other case, an upper bound on the number of rational solutions is obtained. Moreover, we prove that if there are more than $(deg(A)+1)/2$ rational solutions then the equation admits a Darboux first integral.



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