Three-webs determined by a linear differential equation (Q1405706)

The authors show that with a linear first-order ordinary differential equation \(y' + y f(x) = g (x)\) a certain curvilinear three-web \(W\) in the plane is associated. The curvature \(b\) of \(W\) and its covariant derivatives up to the second order satisfy two conditions. The authors also prove that, if for a web \(W\) the above-mentioned two conditions are satisfied, then for this web the differential equation of the form indicated above can be constructed, and \(W\) is associated with this equation.