I am trying to solve the following differential equation


$$f ' (x) = f( f( x ) ),$$


but I have no idea how. I don't think the chain rule is useful for this.


Although I don't think this differential equation is solvable, I'd like to know if there is any interesting approach to solve a differential equation of this kind, or, at least, a non-trivial solution of the equation.



Are there any techniques for solving a differential equation of the form $f ' (x) = f( f( x ) )$?
Nothing is new under the Moon... 


<http://www.artofproblemsolving.com/Forum/viewtopic.php?f=67&t=321705>


