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arXiv · 1512.03615

Liouvillian Solutions of First Order Non Linear Differential Equations

Varadharaj Ravi Srinivasan
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Abstract

Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear homogeneous differential equation over $k$. We apply our results to study liouvillian solutions of first order non linear differential equations and provide generalisations and new proofs for several results of M. Singer and M. Rosenlicht on this topic.

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Varadharaj Ravi Srinivasan. 2015-12-11. Liouvillian Solutions of First Order Non Linear Differential Equations. https://arxiv.org/abs/1512.03615

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