nm

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These are questions asked by nm

Solving this ode, Maple says 

But notice, the xi and eta tangent vectors order is reversed. Maple says pattern is [0,F*G], but shows [F*G,0].

Also, when later using DEtools:-symgen with HINT option, it does not return the above result. Tried both patterns with 0 on left and 0 on right. In both cases symgen does not return what shows above. 

Why is that? Am I doing something wrong? Notice also it says   "way=HINT"  but I am not using way option. Only HINT option, Why is it saying way=HINT? it seems argument passing I  am using is wrong, but do not see why it could be wrong.  This is what help says

Worksheet below

interface(version);

`Standard Worksheet Interface, Maple 2025.2, Windows 10, November 11 2025 Build ID 1971053`

restart;

ode:=diff(y(x),x)*cos(y(x))-cos(x)*sin(y(x))^2-sin(y(x)) = 0;
infolevel[dsolve]:=5;
infolevel[symgen]:=5;

(diff(y(x), x))*cos(y(x))-cos(x)*sin(y(x))^2-sin(y(x)) = 0

5

5

dsolve(ode);

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

differential order: 1; looking for linear symmetries

trying exact

Looking for potential symmetries

trying inverse_Riccati

trying an equivalence to an Abel ODE

differential order: 1; trying a linearization to 2nd order

--- trying a change of variables {x -> y(x), y(x) -> x}

differential order: 1; trying a linearization to 2nd order

trying 1st order ODE linearizable_by_differentiation

--- Trying Lie symmetry methods, 1st order ---

 -> Computing symmetries using: way = 3

 -> Computing symmetries using: way = 4

 -> Computing symmetries using: way = 5

trying symmetry patterns for 1st order ODEs

 -> Computing symmetries using: way = patterns

-> trying a symmetry pattern of the form [F(x)*G(y), 0]

-> trying a symmetry pattern of the form [0, F(x)*G(y)]

-> The symmetry found is [0 exp(-x)*(2*sin(y)^2+cos(y)^2-1)/cos(y)]

<- symmetry pattern of the form [0, F(x)*G(y)] successful

[exp(-x)*(2*sin(y)^2+cos(y)^2-1)/cos(y), 0]

 <- successful computation of symmetries.

y(x) = arctan(-2*exp(x)/(exp(x)*cos(x)+exp(x)*sin(x)+2*c__1), ((2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)+4*c__1^2+(exp(x))^2)*(2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)-3*(exp(x))^2+4*c__1^2))^(1/2)/(2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)+4*c__1^2+(exp(x))^2)), y(x) = arctan(-2*exp(x)/(exp(x)*cos(x)+exp(x)*sin(x)+2*c__1), -((2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)+4*c__1^2+(exp(x))^2)*(2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)-3*(exp(x))^2+4*c__1^2))^(1/2)/(2*cos(x)*sin(x)*(exp(x))^2+4*c__1*sin(x)*exp(x)+4*cos(x)*c__1*exp(x)+4*c__1^2+(exp(x))^2))

infolevel[dsolve]:=0;

0

DEtools:-symgen(ode,y(x),HINT = [ 0,F(x)*G(y)]); #why this does not return the symmetries found by dsolve above?

 -> Computing symmetries using: way = HINT

DEtools:-symgen(ode,y(x),HINT = [ F(x)*G(y),0]); #why this does not return the symmetries found by dsolve above?

 -> Computing symmetries using: way = HINT

DEtools:-symgen(ode)

 -> Computing symmetries using: way = 2

 -> Computing symmetries using: way = 3

 -> Computing symmetries using: way = 4

 -> Computing symmetries using: way = abaco1

[0, exp(-x)*(-1+cos(2*y))/cos(y)]

 <- successful computation of symmetries.

[_xi = 0, _eta = exp(-x)*(-1+cos(2*y))/cos(y)]

 

 

Download symgen_confusion_jan_9_2026.mw

I was searching release notes for some old Maple versions. I found so many broken links on Maple web pages. The first page is https://www.maplesoft.com/products/maple/history/ 

Scrolling down, and starting from Maple 2016 (about half way down the page), all links to the "product press release" are broken. This is the link to the right of each product.  All these links on the right, from 2016 to the end of the page are broken,

Clicking on any of these, sends the user to new broken web page, called https://www.maplesoft.com/company/publications/  titled "Maplesoft media coverage".

This page does not even work. Clicking on "Jump to year" does not open. Clicking in "first page" does nothing. Tried Edge browser on windows 10, also the page does nothing. 

Then I clicked on Maplesoft Media Releases link at top, and now it works.

But jumping to any year before  2016, all the links that show on those pages are broken. Try and see,

For example. jumping to 2015, and clicking on release called "

November 25, 2015"

Gives

This applies to each press release for each year from 2015 to 1997.

Hundreds of links are broken.

There is software which checks broken links, and it is free for windows, called Xenu's Link Sleuth. May be someone at Maplesoft can use it to find all broken links at Maplesoft web site and fix them?

It is not acceptable in this day and age to have a Major software company with a web site full of broken links.

Do not know if this known or reported or not. Just in case. Here is an example where odetest gives internal error when adding integer to assuming. 

Maple 2025.2. Firewall will not let me upload now. Here is code

sol:=y(x) = -4/9*I*(x+1)^(1/4)*(x-1)^(1/4)*2^(1/2)*x^2+4/9*(x+1)^(1/4)*(x-1)^(1/4)*2^(1/2)*x^2+4/9*I*(x+1)^(1/4)*(x-1)^(1/4)*2^(1/2)+1/9*x^4-4/9*(x+1)^(1/4)*(x-1)^(1/4)*2^(1/2)-16/9*I*(x+1)^(1/2)*(x-1)^(1/2)-2/9*x^2+1/9;
ode:=(-x^2+1)*diff(y(x),x)+x*y(x) = x*(-x^2+1)*y(x)^(1/2);
IC:=y(0) = 1;

odetest(sol,[ode,IC]) assuming integer,positive;

Screen shot

There used to be specific web pages, that lists specific update to Maple DE solver.

Only ones I can find are from version 8 to 16. Here are the links below. They start by saying this 

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple8/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple9/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple10/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple11/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple12/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple13/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple14/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple15/de

https://www.maplesoft.com/support/help/Maple/view.aspx?path=updates/Maple16/de

But these do not works for anything after Maple 16 and before 8. i.e. changing the number in the link to 17 or 18 and so on, gives no page found error.

All my search leads to no result.

Are such help pages still present for updates to DE solvers in Maple for versions after Maple 16? WHat link to use to access them?

When I look at web pages under "what is new" it also does not have specific section just for DE solver like those pages had. For example   https://www.maplesoft.com/support/help/maple/view.aspx?path=updates%2Fv2025  does not have specific section just for DE solvers.

I wanted to trick odetest and see what it does. I gave it solution to ode with IC. The solution was in form of implicit solution.

odetest verified it.

Then I solved for y(x) from the implicit solution and passed each now explicit solution to odetest, now it does not verify either one. (two explicit solutions resulted)

I would have thought that odetest to not verify the implicit solution as well. Is this a bug or an expected behavior when using implicit?

Does this mean, to be safe, one should try to solve for y(x) explicitly before using odetest? But sometimes this can be expensive or not possible nor practical to do as implicit solution can be complicated to solve for y(x).

Maple 2025.2 on windows 10.

Firewall now suddently will not let me upload a worksheet again for some reason. Firewall did not have a problem yesterday, but today it complained.

So here code and screen shot

restart;
ode:=2*y(x) + 2*x*y(x)^2 + (2*x + 2*x^2*y(x))*diff(y(x), x) = 0;
IC:=y(0) = 1;
maple_sol:=dsolve([ode,IC]);
#                         maple_sol := ()

my_sol_1:=x*y(x)*(2+y(x)*x)=0;
odetest(my_sol_1,[ode,IC])

#                             [0, 0]

PDEtools:-Solve(my_sol_1,y(x));
map(X->odetest(X,[ode,IC]),[%])

#   [[0, 1], [0, undefined]]

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