"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 you consider only linear operators (aka linear differential equations) then the order is the dimension of the null-space or kernel of the linear operator that produces the differential equation. This takes care of your counter examples with third derivatives.
Example: $y''-y'-y=y''\iff(-\frac{d}{dx}-1)y=0$ so the linear operator we are interested in is $(-\frac{d}{dx}-1)$ which has kernel of dimension 1. Thus even though the differential equation has 2nd order derivatives, it turns out to be a 1st order problem.
