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Question: design question: should Maple dsolve hang on ode which has no analytical solution?

Question:design question: should Maple dsolve hang on ode which has no analytical solution?

nm 11218 Maple 2025
ode dsolve differential-equations timelimit
April 18 2025
1

I wonder what is the general view on this.

Maple tries hard to find analytical solutions by trying different algorithms. Which is very good. But the question is, should it also hang doing this? Should not there be a circuit breaker to prevent the hang?

I mean there must be a limited number of algorithms it tries. So at one point one would expect it will finish and return either no solution or the solution it found.

For this Abel ode   y'=x+y^3, which is known not to be solvable, Maple hangs on 

           > Step 2: calculating resultants to eliminate F and get candidates for 

I waited for almost one hour. Clearly this indicates a problem internally. Right?

There should be some internal checks to prevent this hang I would think.  I do not know where it actually hangs, since trace only shows the last step above.

It will good to find out the cause of the hang and add code to prevent this in a future version of Maple dsolve to make it more robust.

btw, using that another software, it returns instantly on this ode with no solution. May be the other software did not try as hard, but at least it did not hang :)

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1861 and is the same as the version installed in this computer, created 2025, April 10, 15:58 hours Pacific Time.`

> 

restart;
> 

infolevel[dsolve]:=5;
ode:=diff(y(x),x)=x+y(x)^3;
sol:=dsolve(ode,y(x))

5

diff(y(x), x) = x+y(x)^3

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

trying inverse linear

trying homogeneous types:

trying Chini

Chini's absolute invariant is: (1/27)/x^5

differential order: 1; looking for linear symmetries

trying exact

trying Abel

The relative invariant s3 is: x

The first absolute invariant s5^3/s3^5 is: 1/x^5

The second absolute invariant s3*s7/s5^2 is: 0

...checking Abel class AIL (45)

...checking Abel class AIL (310)

...checking Abel class AIR (36)

...checking Abel class AIL (301)

...checking Abel class AIL (1000)

...checking Abel class AIL (42)

...checking Abel class AIL (185)

...checking Abel class AIA (by Halphen)

...checking Abel class AIL (205)

...checking Abel class AIA (147)

...checking Abel class AIL (581)

...checking Abel class AIL (200)

...checking Abel class AIL (257)

...checking Abel class AIL (400)

...checking Abel class AIA (515)

...checking Abel class AIR (1001)

...checking Abel class AIA (201)

...checking Abel class AIA (815)

Looking for potential symmetries

... changing x -> 1/x, trying again

Looking for potential symmetries

The third absolute invariant s5*s7/s3^4 is: 0

 ->         ======================================

 ->             ...checking Abel class D (by Appell)

 -> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 1

*** No disqualifying factor on F was found ***

 -> Step 2: calculating resultants to eliminate F and get candidates for C

 

 

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