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);

Over the past year, I have spent a lot of time talking to educators, researchers, and engineers about AI. The feeling is almost universal: it is impressive, it is helpful, but you should absolutely not trust it with your math even if it sounds confident.

That tension between how capable AI feels and how accurate it actually is has been on my mind for months. AI is not going away. The challenge now is figuring out how to make it reliable.

That is where Maple MCP comes in.

Maple MCP (Model Context Protocol) connects large language models like ChatGPT, Claude, Cohere, and Perplexity to Maple’s world-class math engine.

When your AI encounters math, your AI can turn to Maple to handle the computation so the results are ones you can actually trust.

It is a simple idea, but an important one: Maple does the math and the AI does the talking. Instead of guessing, the AI can be directed to call on Maple whenever accuracy matters.

Model Context Protocol (MCP) is an emerging open standard that allows AI systems to connect to external tools and data sources. It gives language models a structured way to request computations, pass inputs, and receive reliable outputs, rather than trying to predict everything in text form.

Here is a high-level view of how MCP fits into the broader ecosystem:

MCP lets an AI system connect securely to specialized services, like Maple, that provide capabilities the model does not have on its own.

If you want to learn more about the MCP standard, the documentation is a great starting point: Model Context Protocol documentation

Here is a glimpse of what happens when Maple joins the conversation:

Depending on the prompt, Maple MCP can evaluate expressions symbolically or numerically, execute Maple code, expand or factor expressions, integrate or solve equations, and even generate interactive visualizations. If you ask for an exploration or an activity, it can create a Maple Learn document with the parameters and sliders already in place.

As an example of how this plays out in practice, I asked Maple MCP:

“I'd like to create an interactive math activity in Maple that allows my students to explore the tangent of a line for the function f(x) = sin(x) + 0.5x for various values of x.”

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In full disclosure, I did have to go back and forth a bit to get the exact results I wanted, mostly because my prompt wasn’t very specific, but the process was smooth, and I know it will only get better over time.

What is exciting is that this does not replace the LLM; it complements it. The model still explains, reasons, and interacts naturally. Maple simply steps in to do the math—the part AI cannot reliably do on its own.

We have opened the Maple MCP public beta, and I would love for you to try it.

Sign up today and we will send you everything you need to get started!

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:

My student, David Wei, has ported Andrew Hicks's MOISE package to Maple 2025:

GitHub - david-wei-01001/MOISE-for-Maple-2025: MOISE that is compatible with the newest Maple 2025 Engine

Regards,

Gerald Penn

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.