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Question: why DEtools:-odeadvisor returns linear on this ode? This causes call to convertAlg to FAIL

Question:why DEtools:-odeadvisor returns linear on this ode? This causes call to convertAlg to FAIL

nm 8552 Maple 2022
differential-equations odeadvisor
September 17 2022
2

I changed today my code to use DEtools:-odeadvisor(ode,y(x),[linear]); to check that the ode is linear or not before calling DEtools:-convertAlg 

The problem is that sometimes the advisor returns _linear on what is not linear ode (at least the way it is originally written). Here is an example

              (x+y(x))*diff(y(x),x) = 0;

From help page:

 

In the event that convertAlg cannot isolate for the proper list form (for instance, if the DE is not a linear ODE) then FAIL is returned.

 

So now I am worried  that using odeadvisor to check for linear ode is not the right method.

Is there a build-in method in Maple to check if an ode is linear or not? (I do have my own code to do this, but I thought it is better to use a buildin method, as it will be more robust).

Should DEtools:-odeadvisor(ode,y(x),[linear]) have returned _linear in this case?

> 

interface(version);

`Standard Worksheet Interface, Maple 2022.1, Windows 10, May 26 2022 Build ID 1619613`

> 

ode:=(x+y(x))*diff(y(x),x) = 0;
DEtools:-odeadvisor(ode,y(x));
#check if linear ODE
DEtools:-odeadvisor(ode,y(x),[linear]);

(x+y(x))*(diff(y(x), x)) = 0

[_quadrature]

[_linear]

> 

DEtools:-convertAlg(ode,y(x));

FAIL

> 

 

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