I have a nonlinear differential equation of the kind:
$ f(\ddot{x},\dot{x},x) =0$
I would like to know if there is always a way to write such a differential equation in a form like:
$ \dot{y} = g(y) $
that is to put the equation in the form of a set of first order differential equations. What sort of complications arise in the nonlinear case compared to the linear second order ordinary differential equation? Also, what problems may arise when there are terms like $ \dot{x} x $ ?