Integrating the Jacobian equation

Airton von Sohsten de Medeiros; Ráderson Rodrigues da Silva

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arXiv · 1409.7059

Integrating the Jacobian equation

Airton von Sohsten de Medeiros·Ráderson Rodrigues da Silva

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Abstract

We show essentially that the differential equation $\frac{\partial (P,Q)}{\partial (x,y)} =c \in {\mathbb C}$, for $P,\,Q \in {\mathbb C}[x,y]$, may be "integrated", in the sense that it is equivalent to an algebraic system of equations involving the homogeneous components of $P$ and $Q$. Furthermore, the first equations in this system give explicitly the homogeneous components of $Q$ in terms of those of $P$. The remaining equations involve only the homogeneous components of $P$.

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Airton von Sohsten de Medeiros, Ráderson Rodrigues da Silva. 2014-09-16. Integrating the Jacobian equation. https://arxiv.org/abs/1409.7059

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