Question: Why Maple odeadvisor says this ode is dAlmbert when it is missing x on the RHS?

dAlmbert ode has the form


Also from Maple own help page, it agrees with Wikipedia and says:


Now, given this ode


Then clearly the above is not dAlmbert. Right? it is missing the x. But odeadvisor says it is:


What Am I missing here?


These are the rules I know about this ode. For y=x f(p)+ g(p). 

g(p) can be zero, yes, but in this case, f(p) has to be nonlinear in p for it to be dAlembert (else it will be either separable or linear.

I did not think f(p) can be zero and it remains dAlermber, even if g(p) remains nonlinear in p. So y=g(p) can not be dAlembert, even if g(p) is nonlinear.

May be Maple uses its own definition of dAlembert?. I do not know. This will be new definition to me. Is there a reference that mentions this case of y=g(p) classified as dAlembert for nonlinear g?

Maple 2022.1 on windows 10

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