I made up a problem where this ODE appears and is the solution to that, well I'm supposed to say what I've tried but I'm not even at university and never even taken calculus class. However I'm a bit familiar to integration and solving first order ODE, I made a quick google search but didn't found any ODE like this unfortunately. Basically I want the family of functions whose the tangent of the function is the same as its derivative.
It's the same to solve y=arctan(y'), no problem in worrying about the domain.
How can I "generalise" these kind of solutions?: tan(g(y,x))=y' or tan(g(y))=y'
Wolfram alfa couldn't help me. Can the solution be expressed in terms of elementary function? if not how would it look like?