Question: should odeadvisor depend on form of ODE?

I use odeadvisor a lot to tell me the type of the ode. It is one of the best tools in Maple.

But sometimes it overlooks some types of ODE's, if the ODE is written in different way. This does not happen alot. Here is an example

ode:=diff(y(x),x) = (2*x+y(x))/(3-x+3*y(x)^2);
DEtools:-odeadvisor(ode)


And advisor says it is rational, which is correct. 

But it does not also say it is exact. By rewriting as follows, it now see it is exact as well as rational:

ode2:=(denom(rhs(ode)))*diff(y(x),x)-(numer(rhs(ode)))=0;
DEtools:-odeadvisor(ode2);

And now it says [_exact, _rational]. It is the same ODE, just written different.

This is not a complaint about the advisor, I know it is not easy to figure the type of the ODE under different trasformations, but may be something to look into to improve it to be able to detect more types.

Maple 2020.1 

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