How to explain this strange behavior?   odetest(sol,ode) does not give zero. But odetest(sol,[ode,IC]) gives [0,0]

Same solution and same ode. Why adding IC, now odetest says solution verifies the ode, but without adding IC, it does not give zero right away. I know I can simplify the result to zero. But the point is that it should have given zero right away, because that is what it did when adding IC.

Should it not have given zero in first case also?

Can't upload worksheet due to security. Here is code and screen shot

ode := diff(y(x),x) + cos(1/exp(2*x))*y(x) = sin(1/exp(x));
IC := a*D(y)(x0)+c*y(x0) = b*y0;
sol:=y(x) = ((-cos(exp(-2*x0))*a + c)*Int(sin(exp(-tau))*exp(-1/2*Ci(exp(-2*tau))), tau = 0 .. x0) + Int(sin(exp(-tau))*exp(-1/2*Ci(exp(-2*tau))), tau = 0 .. x)*(cos(exp(-2*x0))*a - c) + exp(-1/2*Ci(exp(-2*x0)))*(a*sin(exp(-x0)) - b*y0))*exp(1/2*Ci(exp(-2*x)))/(cos(exp(-2*x0))*a - c);

odetest(sol,ode);

#not zero

#now

odetest(sol,[ode,IC]);

#gives [0,0]

By symbolic regression I mean an algorithm that determines a model (fit function) that fits best to a data set.

Are there any commands, packages, libraries or MaplesPrime post that are helpful in this regrad?

Edit: For the data set below a symbolic regression algortihm returns "simple" models (formulas)  that use a "minimal" number of terms.

Download regression_dataset.mw

I do not understand the following typesetting example from this helpage.

Download Typeset.mw

Why the Typeset call when the output does not change. Is the helppage maybe broken? It says Examples but lists only one.

If MapleSoft read this: Some more typesetting examples would be helpfull.

I recently read something in another forum about solving a simple ordinary differential equation as an initial value problem (file attached). An unexpected solution behavior was interpreted there as a weakness of the software. However, upon closer inspection, the cause is different, and as a software novice, I cannot determine it myself.

Therefore, my question is:

Is there a way, using Maple, to check the Lipschitz condition in the neighborhood of the initial value before starting the solution of an explicit first-order system of differential equations as an initial value problem?

DGL_test.mw

i try to find the parameter in this equation but some issues show up which i am not sure i can fix that or not? there is any way for finding thus parameters?

test-F-p.mw

Could someone please check if these are new in Maple 2025.2? I am on windows 10.

eqs:=[_C1+_C2 = 0, _C1*exp(3^(1/2)*((cos(1/6*Pi*3^(1/2))-1)*(cos(1/6*Pi*3^(1/2))+1))^(1/2)/(cos(1/6*Pi*3^(1/2))-1)^(1/2)/(cos(1/6*Pi*3^(1/2))+1)^(1/2)*ln(cos(1/6*Pi*3^(1/2))+(cos(1/6*Pi*3^(1/2))^2-1)^(1/2)))+_C2*exp(-3^(1/2)*((cos(1/6*Pi*3^(1/2))-1)*(cos(1/6*Pi*3^(1/2))+1))^(1/2)/(cos(1/6*Pi*3^(1/2))-1)^(1/2)/(cos(1/6*Pi*3^(1/2))+1)^(1/2)*ln(cos(1/6*Pi*3^(1/2))+(cos(1/6*Pi*3^(1/2))^2-1)^(1/2))) = 4];
c:=[_C1, _C2];
solve(eqs,c);

#Error, (in convert/real_rat) too many levels of recursion

And

eqs:= [3^(1/4*3^(1/2))*exp(3/4*Pi)*_C1-1/3*exp(3/4*Pi)*3^(-1/4*3^(1/2)+1/2
)*_C2 = 1, _C1/(cos(1/3*Pi*3^(1/2))-1)^(1/4)/(cos(1/3*Pi*3^(1/2))+1)^(1/4)*exp(
3/4*Pi-1/2*Pi*3^(1/2))*(cos(1/3*Pi*3^(1/2))^2-1)^(1/4)*3^(1/4*3^(1/2))*((cos(1/
3*Pi*3^(1/2))^2-1)^(1/2)+cos(1/3*Pi*3^(1/2)))^(1/2*3^(1/2))-_C2*3^(-1/2-1/4*3^(
1/2))/(cos(1/3*Pi*3^(1/2))-1)^(1/4)/(cos(1/3*Pi*3^(1/2))+1)^(1/4)*(cos(1/3*Pi*3
^(1/2))^2-1)^(1/4)*exp(3/4*Pi-1/2*Pi*3^(1/2))*((cos(1/3*Pi*3^(1/2))^2-1)^(1/2)+
cos(1/3*Pi*3^(1/2)))^(-1/2*3^(1/2)) = 5*exp(-1/2*Pi*3^(1/2))]:
c:=[_C1, _C2];

solve(eqs,c)

#Error, (in convert/real_rat) too many levels of recursion

And

eqs:=[3^(1/2*3^(1/2))*exp(1/2*Pi)*_C1-1/6*3^(-1/2*3^(1/2)+1/2)*exp(1/2*Pi
)*_C2 = 5, _C1/(cos(1/6*Pi*3^(1/2))-1)^(1/4)/(cos(1/6*Pi*3^(1/2))+1)^(1/4)*exp(
1/2*Pi-1/6*Pi*3^(1/2))*(cos(1/6*Pi*3^(1/2))^2-1)^(1/4)*3^(1/2*3^(1/2))*((cos(1/
6*Pi*3^(1/2))^2-1)^(1/2)+cos(1/6*Pi*3^(1/2)))^(3^(1/2))-1/6*_C2*3^(-1/2*3^(1/2)
+1/2)/(cos(1/6*Pi*3^(1/2))-1)^(1/4)/(cos(1/6*Pi*3^(1/2))+1)^(1/4)*exp(1/2*Pi-1/
6*Pi*3^(1/2))*(cos(1/6*Pi*3^(1/2))^2-1)^(1/4)*((cos(1/6*Pi*3^(1/2))^2-1)^(1/2)+
cos(1/6*Pi*3^(1/2)))^(-3^(1/2)) = 2*exp(-1/6*Pi*3^(1/2))]:
c:=[_C1, _C2];

solve(eqs,c)

Trace shows they are coming from Algebraic: best unknown/equation

Cannot upload worksheet due to security. Here is screen shot

Variation of (a) Skin friction ∂W/∂Z​, (b) Heat Transfer ∂θ/∂Z​, and (c) Mass Transfer ∂ϕ/∂Z​ for γ=10.0, Pr=7.0, ε=1.0, Nt=0.4, and Nb=0.2.

how to get this values by solving the PDE by using the pdsolve method 

Variation of (a)W(b) θ and (c) ϕ for different value of γ when ε = 10.0, Nb = 0.4, ε = 10.0, Sc = 0.5 and Pr = 7.0.
consider X as 0.1

plume_work.mw

Could someone please check if this error happens in earlier versions of Maple? I have only Maple 2025.2 on Windows.

Unable to upload worksheet due to new security. Here is the code to run

restart;
integrand:=-3*(Pi-2*arcsin(tau))*(tau+1)^(1/2)*(tau+(tau^2-1)^(1/2))^(2*(tau^2-1)^(1/2)/(tau-1)^(1/2)/(tau+1)^(1/2))*(tau-1)^(1/2)*(-16/3*tau^2+Pi-2*arcsin(tau)+8/3)/(4*tau^2-4);

int(integrand,tau)

The error is 

Update dec 12, 2025

Here is another int() error. In Maple 2025.2.  It comes from

RationalTrigOnly: case ratpoly*trig(arg)
Error, (in unknown) too many levels of recursion
 

I still can not upload worksheet. So here is the code followed by screen shot

integrand:=-(tau+(tau^2-1)^(1/2))^(1/2*(tau^2-1)^(1/2)/(tau-1)^(1/2)/(tau+1)^(1/2))*(64*tau^4+Pi^2-4*Pi*arcsin(tau)+4*arcsin(tau)^2-64*tau^2+8)*(tau-1)^(1/2)*(tau+1)^(1/2)/(16*tau^2-16);

int(integrand,tau);
....
TrigOnly: case of integrand containing trigs
RationalTrigOnly: case ratpoly*trig(arg)
Error, (in unknown) too many levels of recursion

I did not make new question as this seems to be same source of error but can not be sure now.

Second update DEC 12, 2025

Here is 3rd one. Seems also the same. comes from RationalTrigOnly: case ratpoly*trig(arg)

integrand:=-(tau + sqrt(tau^2 - 1))^(2*sqrt(tau^2 - 1)/(sqrt(tau - 1)*sqrt(tau + 1)))*(Pi - 2*arcsin(tau))*(12*tau^2 + Pi - 2*arcsin(tau) - 6)*sqrt(tau - 1)*sqrt(tau + 1)/(16*tau^2 - 16);

int(integrand,tau);

Why one is no longer able to upload worksheet here showing a problem? I found an internal error in int() but can't upload worksheet.

When I click on the green arrow and select my worksheet, I get this message

What is going on? I am on windows 10 and I tried 2 different browsers. So the problem is on the Mapleprimes site.

Can anyone else try to upload a worksheet to test to see if they get same problem?

Currently, when I have solution to an ode, say y(x)=sin(x)+_C1 and have some initial condition, then to solve for _C1,  I manually substitute the solution into the IC and replace each x by x0 and replace each derivative manually and so on.

This is because I could not find automatic way to do this. Using another software, it is possible to automate this by writing the solution using the  y -> Function[{x}, ...] syntax. But in Maple, I was not sure how to do the same.

Here is a simple made up example. 

sol:= y(x) = sin(x)+_C1;
IC := a*D(y)(x0)+c*y(x0)= b*y0+exp((D@@2)(y)(x0));

The goal is to replace the solution (which is function y(x)) into the IC, and automatically replace all its derivatives and replace x by x0 then solve for _C1 from the equation that results.

Now I do this manually like this

eval(IC,[ y(x0)=eval(rhs(sol),x=x0), 
          D(y)(x0)=eval(diff(rhs(sol),x),x=x0), 
         (D@@2)(y)(x0)= eval(diff(rhs(sol),x$2),x=x0) ])

which gives

But this is too much work.

Using the other software, I can do the above much more easily like this

sol = y -> Function[{x}, Sin[x] + C[1]]
ic = a*y'[x0] + c*y[x0] == b*y0 + Exp[y''[x0]];
ic /. sol

I looked at algsubs, dchange, or making the solution as function instead, and so on but could not emulate the y -> Function[{x}, Sin[x] + C[1]] method in Maple.

What would be similar method in Maple to do the above automatically?  May be there is already builtin function in Maple?

I frequently receive this message after installing the most recent Maple update:

Can anyone help me with this? Thank you so much for your valuable support.

is it possible to collect using pattern? For example, given 

How to tell Maple to collect on  r^power terms to produce

This came up in another forum here  and using that other software, it is possible to ask collect to collect on pattern r^_

Is there a way in Maple to collect on all powers of r in the above? Here is worksheet

Download collect_using_pattern.mw

Using that other software:

In the below plot switches between to solutions of a RootOf expression when the plot range starts at zero.

plot3d on the other hand sticks to one root.

Why is that and how to get a plot starting at zero showing only one root?

Download plot_of_RootOf.mw

Hello,

I have upgraded to maple 2025, but the ui fonts are too small and very thin. I went to Files -> Options -> Interface -> Default Zoom, thet sat it up to 150%. It only changed the document area not the UI options. This solution used to work with Maple 2024. I am on ubuntu 22.04.

i did my try to sketch the best shape of graph by existing code but the 3D shape in matlab is not what i am looking and is  not intresting for this kind of plot so i want use and design a better shape of 3D plot for thus contour  i need help for that 

plot-help.mw