nm

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These are questions asked by nm

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]]

I noticed today only 2 cases where calling simplify, with no options, made things worst.

Just trying to understand why.

Here is one example. Solved an ode. when calling odetest on this solution, it gives zero. But if the solution is simplified first, then odetest no longer gives zero. And it is actually hard to find a trick to make it become zero so far.

But the question is: Is this to be expected sometimes? I use simplify sporadically, but like to get smaller  expression at one point. But now I am not sure if I should even do that.

Could this be a problem in simplify itself somehow?

Here is an example.

interface(version);

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

restart;

ode:=diff(y(x), x) = y(x)*(-1 - x^(2/(ln(x) + 1))*exp(2*ln(x)^2/(ln(x) + 1))*x^2 - x^(2/(ln(x) + 1))*exp(2*ln(x)^2/(ln(x) + 1))*x^2*ln(x) + x^(2/(ln(x) + 1))*exp(2*ln(x)^2/(ln(x) + 1))*x^2*y(x) + 2*x^(2/(ln(x) + 1))*exp(2*ln(x)^2/(ln(x) + 1))*x^2*y(x)*ln(x) + x^(2/(ln(x) + 1))*exp(2*ln(x)^2/(ln(x) + 1))*x^2*y(x)*ln(x)^2)/((ln(x) + 1)*x);

diff(y(x), x) = y(x)*(-1-x^(2/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1))*x^2-x^(2/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1))*x^2*ln(x)+x^(2/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1))*x^2*y(x)+2*x^(2/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1))*x^2*y(x)*ln(x)+x^(2/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1))*x^2*y(x)*ln(x)^2)/((ln(x)+1)*x)

sol_1:=dsolve(ode);

y(x) = exp(-(1/4)*x^4)/(x^(-2*ln(x)/(ln(x)+1))*exp(-(1/4)*(x^4*ln(x)+x^4+4*ln(ln(x)+1)*ln(x)-8*ln(x)^2+4*ln(ln(x)+1))/(ln(x)+1))*ln(x)^2+2*x^(-2*ln(x)/(ln(x)+1))*exp(-(1/4)*(x^4*ln(x)+x^4+4*ln(ln(x)+1)*ln(x)-8*ln(x)^2+4*ln(ln(x)+1))/(ln(x)+1))*ln(x)+x^(-2*ln(x)/(ln(x)+1))*exp(-(1/4)*(x^4*ln(x)+x^4+4*ln(ln(x)+1)*ln(x)-8*ln(x)^2+4*ln(ln(x)+1))/(ln(x)+1))+ln(x)*c__1+c__1)

odetest(sol_1,ode)

0

sol_2:=simplify(sol_1);

y(x) = 1/((ln(x)+1)*(exp((1/4)*x^4)*c__1+1))

odetest(sol_2,ode);

c__1*x^(ln(x)/(ln(x)+1)+3/(ln(x)+1))*exp(2*ln(x)^2/(ln(x)+1)+(1/4)*x^4)/((ln(x)+1)*(exp((1/4)*x^4)*c__1+1)^2)-c__1*x^3*exp((1/4)*x^4)/((ln(x)+1)*(exp((1/4)*x^4)*c__1+1)^2)

 

 

Download why_simplify_changes_things_at_dec_27_2025.mw

Notice how much simpler the solution becomes after calling simplify. I'd like to use that. But for some reason, odetest now fails to verify the simpler version. Which tells me simplify did something which made the solution not valid.

Here is second example, where calling simplify in betwen did not give zero as expected.

restart:

f := sqrt(1 + sin(x)^2);
F := int(f, x):
df := diff(F, x):
simplify(df - f);

(1+sin(x)^2)^(1/2)

0

restart;

f := sqrt(1 + sin(x)^2);
F := int(f, x):
F := simplify(F):
df := diff(F, x):
simplify(df - f);

(1+sin(x)^2)^(1/2)

-csgn(1, cos(x))*sin(x)*EllipticE(sin(x), I)

 

 

Download why_simplify_changes_things_at_dec_27_2025_V2.mw

Just trying to understand why this happens and if this is something that could happen sometimes? May be one should avoid calling simplify in middle of computation and let the user decide if they want to simplify the final result or not?

I do not remember now if this came up before or not. But this has been a problem in Maple for years.

when doing infolevel[dsolve]:=5 and call dsolve(), some of the display on the screen is missing commas and multiplication sign and who know what else. Since it is all replace by space.

This happens only to part of the display. Here is an example (must use restart each time to see the full display)

restart;
ode:=diff(y(x),x) = (-y(x)^2+4*a*x)^2/y(x); 
infolevel[dsolve]:=5;
dsolve(ode);

Here is the output. Using worksheet, V 2025.2 on windows 10 (I am only showing part of the output which has the problem)

Looking at the line where is says "-> Calling odsolve ". Notice the rest. diff(diff(y(x) x) x)  should be diff(diff(y(x),x),x)  and the end of the line has diff(y(x) x)) y(x)  . So one can guess this should be  diff(y(x),x))*y(x) or it could be diff(y(x),x))/y(x) or may be something else.

THis cause a problem when trying to copy it and use it to try it.

Is there something one can do  in settings to fix this part of the display? so nothing is replace by space?

Maple 2025.2 on windows 10

I also tried this in document mode instead of worksheet. Same result. 

Update

Found where this comes from. From `odsolve/2` proc, line 21.

THis is how to see it.

restart;

infolevel[dsolve]:=5;
ode:=diff(y(x),x)=x*y(x)+1/y(x)+y(x)^3;
stopat(`odsolve/2`);
dsolve(ode)

 

Now the debugger will come up. Then do in the debugger:

stopat 21

Click continue, you will now stop at this line

In the worksheet it now shows as

So something in 

 `ODEtools/userinfo`(2,dsolve,`-> Calling odsolve with the ODE`,A);

Is not right. Also the last y(x) was meant to be second item in A which is expression sequence. But in worksheet it all display on one line with no commas between.,

So better formating in ODEtools/useinfo is needed here. For some reason, commas are all replaced by spaces.

 

 

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