Fyi, Reported to WRI in case it is a bug. [CASE:4288939]
Is this supposed to happen?
ClearAll[y, x, a]; DSolve[(1+(y'[x])^2)(ArcTan[y'[x]]+a x)+y'[x]==0,y[x],x]
$ on the variable
K. I do not think I've seen this before, but may be I did and forgot.
Why it happens and is this considered a defect?
Btw, in V 11.3, this does not happen because the ODE is not solved
So this seems to be something new in V12.
V 12 on windows 10.