Submission date: 15 July 2016.

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) where f 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.

Mathematics Subject Classification:

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Full text arXiv 1607.04387: pdf, ps.