"The order of a differential equation is the highest derivative in the equation". What's wrong with this statement? I am asked the following

"The order of a differential equation is the highest derivative in the equation". What's wrong with this statement? 

I've checked my text and several other sources, and the statement above is what they have used to define the order of a differential equation. So what am I missing here that makes this statement false or insufficient?
One counter example I do see to the definition is $$y'''+y''x=y'''+2y$$
Since 
$$y'''+y''x=y'''+2y \Leftrightarrow xy''-2y=0$$

If the given ODE can be written in the form
$$y^{(n)}(t)=F\bigl(t,y(t),y'(t),\ldots,y^{(n-1)}(t)\bigr)$$ then it is of order $n$. If the  ODE is given in the form
$$G\bigl(t,y(t),y'(t),\ldots,y^{(n)}(t)\bigr)\equiv0$$
then it is an implicit ODE of order $n$, and the standard theorems about ODE's cannot be applied without caution.
