  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.
