Disintegrated order one differential equations and algebraic general solutions

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.

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

References in corpus (2)

• Order 1 strongly minimal sets in differentially closed fields
• Differentials over differential fields