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I converted an ode using the built-in "convert" tool to check some calculations I had done by hand. To my surprise, there was an inconsistency. I converted the ode using PDEtools[dchange], reproducing the steps I had followed manually, and they checked out. So my question is: is there a sign error in convert? (and therefore a bug) or are both conversions correct, and if so are there any lessons to be learned? (is it related to the equation's symmetries?)

Thanks for your comments.

There was a lengthy series of posts [link], in late 2008, concerning the paper of Demetrios Panyotounakos that claimed to have solved a large class of Abel equations.  As I read the posts, it would seem that the final conclusion had not yet occurred, as to the validity of his claim. 

In particular there were questions to Edgardo Cheb-Terrab as to why this...