FYI -- This paper discusses the solution of a differential equation (y in terms of x) as well as its inverse function (x in terms of y). The particular example shows x as a cubic polynomial in y, so the inverse is solvable in radicals. I'm curious to know if this particular way of looking at things would provide more insights into the solvability of quartic, quintic, etc., equations. http://online.watsci.org/abstract_pdf/2019v26/v26n3a-pdf/4.pdf EXTENDING THE ALGEBRAIC MANIPULABILITY OF DIFFERENTIALS Jonathan Bartlett 1 and Asatur Zh. Khurshudyan 2 1 The Blyth Institute jonathan.bartlett@blythinstitute.org Broken Arrow, OK, USA 2 Institute of Mechanics, NAS of Armenia Abstract. Treating differentials as independent algebraic units have a long history of use and abuse. It is generally considered problematic to treat the derivative as a fraction of differentials rather than as a holistic unit acting as a limit, though for practical reasons it is often done for the first derivative. However, using a revised notation for the second and higher derivatives will allow for the ability to treat differentials as independent units for a much larger number of cases.