English

Disintegrated order one differential equations and algebraic general solutions

Logic 2017-10-09 v2

Abstract

We generalize results of Rosenlicht to give a necessary and sufficient condition for when order one differential equations of the form D(x)=f(x)D(x) = f(x) where ff is a rational function is orthogonal to the constants. Following the main results of the paper, we also explain the connection between algebraic general solutions and weak orthogonality to the constants; a portion of this discussion is given in the appendix, written jointly with Joel Nagloo and Ngoc Thieu Vo.

Keywords

Cite

@article{arxiv.1607.04387,
  title  = {Disintegrated order one differential equations and algebraic general solutions},
  author = {James Freitag},
  journal= {arXiv preprint arXiv:1607.04387},
  year   = {2017}
}

Comments

Appendix joint with Joel Nagloo and Ngoc Thieu Vo. There is an error in the main theorem of the paper

R2 v1 2026-06-22T14:55:29.083Z