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Question: Strange result by odeadvisor. It says it is Chini when it is Quadrature

Question:Strange result by odeadvisor. It says it is Chini when it is Quadrature

nm 9899 Maple 2024
ode differential-equations odeadvisor
August 30 2024
0

For me this result is suspicious. What do you think? 

This ode diff(y(x),x) = f*y(x)^4+g*y(x)+h; is clearly quadrature, since I did not tell Maple that f,g,h depend on x. So this can be solved by just integration. But when asking odeadvisor if it is Chini, it says yes. When asking it what type it is, now it says it is quadrature.

Am I missing something here? I was expecting [NONE] when asking it if it is Chini.

Yes, the ode has the form of Chini, which is   y'=f(x)*y^n + g(x)*y + h(x), where n=4 here. But if f,g,h do not depend on x, then this is now just quadrature. Right? Calling it Chini is little misleading I think.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1796 and is the same as the version installed in this computer, created 2024, August 29, 14:22 hours Pacific Time.`

> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

restart;
> 

ode:=diff(y(x),x) = f*y(x)^4+g*y(x)+h;
DEtools:-odeadvisor(ode,y(x),[Chini]);

diff(y(x), x) = f*y(x)^4+g*y(x)+h

[_Chini]

> 

DEtools:-odeadvisor(ode,y(x))

[_quadrature]

> 

dsolve(ode,y(x),[quadrature]);

x-Intat(1/(_a^4*f+_a*g+h), _a = y(x))-c__1 = 0

> 

dsolve(ode,y(x),[Chini]);

y(x) = -RootOf(Intat(g^4/(_a^4*f*h^3-_a*g^4+g^4), _a = _Z)+g*x+c__1)*h/g

 

 

Download question_on_advisor_august_28_2024.mw

Notice another problem in this solutions. If g=0, then the Chini solution gives divison by zero now, while the quadrature solution still works.
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