I am trying to find the value of $y''$ when $x= 0$ for $xy+e^y = e$
This seems pretty simple and straightforward to me
$xy' + y + e^y y' = 0$
then derive again
$xy'' + e^y y'' = -e^y y'y' - y'$ which is not correct and I do not know why, infact the book gets some crazy answer with just an e in it which seems impossible to me since e will go away.