@Carl Love 

It is not Riccati.  Riccati has this short form  y'=q(x)+y^2, where q here must be function of x and not just a constant or parameter.

Wikipedia writes q0(x)  to indicate this but may be it should also made it clear that q0 must depend on x.  Not all the q's have to be function of x, but at least one of them must.

The ode  y'=3+y^2 is quadrature (because it solved by just integration), but y'=x+y^2 is riccati.

Another example

And another

your ode is not Riccati. This is basic quadrature.

Download dsolve_may_19_2025.mw

@delvin 

I want to define the expression diff(H(xi), xi, xi)/H(xi)^2 as a new variable

Then why you said in your question you wanted the coefficient of the above to be zero?

Ok,, try this. if you want to eliminate H(xi), then try solving the ode  H'/H^2=Z for H and then use dchange to chnage the dependent variable H to Z.

The new ode will be in term of Z(xi) only and no H(xi) in it. 

Again, do not know if this is what you meant. If not, then may be someone else can better guess than I am able to.

Download repl_may_19_2025_V2.mw

@delvin 

 I want to remove the derivatives in eq 2 and the new function will not have any derivative terms at all.

If this is what you want, then why not just set diff(H(xi), xi) to zero in each term that has it? Looking at your eq2, this will leave only 2*a3*c^2*A/H(xi)^2 term.

@vv 

Closed all of Maple, open Maple, open worksheet. No interface call,  nothing, just the timelimit call, this is the result 

Download simplify_may_17_2025_v2.mw

Do not know why now it gives such large output. Strange. But no crash.

And then closed Maple, started again, and now just called simplify with no timelimit. Waited 2 mins, then stopped kernel using the button on lower left corner. it worked. computation stopped.

No problem for me on Linux, Maple 2025 with ST 17.

I also was able to stop the kernel by clicking on lower left red botton. Timelimit also works on this.

worksheet below

Download simplify_may_17_2025.mw

@acer 

I myself only export to pdf or if not possible to .ps (this is from any application, not just Maple) and then for HTML use, convert the PDF to svg using the Linux builtin command pdf2svg which comes with any Linux distro or can be easily installed on Linux if it is not already there.

pdf2svg  is  a tiny command-line utility using Cairo and Poppler 
to convert PDF documents into SVG files."

Always export to vector based format and not raster based format. So try to export to postscript or pdf and not to png or jpeg. 

@dharr 

Thanks. This is all done in code, and code does not know that there is LambertW function in solution.

Code tries positive and negative assumptions among other things, but not x>1 or x<1

I'll add code to check if solution or residue has LambertW and in this case add assumptions x>1 and x<1 (but also code does not know what the argument to LambertW in the solution, so it will need to do more than this, i.w. the function can be W(-exp(-2*x)) instead of W(-exp(-x)) as in this case, and also there can be more than one LambertW in the solution with different arguments, so finding the correct domain can quickly become complicated). Again, all of this is done in code. Can't look at screen and decide what to do.

It will be nice if odetest itself can do all of this work and give result with conditions to the user. i.e. an answer with piecewise with 0 where it is valid solution and not zero when it is not. 

Many times I find that solving an ode is simpler than verifying the solution is correct!

this looks like a bug as help clearly says

"The convert(A, Vector) function converts the parameter A into a Vector.
"The orientation of the result can be specified via the parameter o. The default orientation is column."

Also below it says

"If A is a 1-dimensional array or Array, a list, a vector or a Vector, it is simply passed directly to the Vector constructor"

but Vector([1, 2, 3]) gives column vector.

@C_R 

I see. But if the reason it timedout for you when you run in B.M. (battery mode) is because Maple was slower and the 30 seconds was reached before entering the DLL, then this will not help me. It is then just by chance. It is like me setting timelimit of 2 seconds instead of 30 second. If you change your timelimit from 30 seconds to say 2 minutes, does it still not hang for you in B.M. mode?

What I do not understand is why timelimit does not work when code is inside DLL. Assuming for now that the hang happens inside this GMP DLL. does timelimit have no effect in this case because the code is inside dynamic linked library?

I can'f find definite answer or information on this now using google.

But there has to be a way to terminate a call, even if it is inside DLL which is faulty and hangs.

I am sure someone inside Maplesoft knows the answer for this and could comment and explain what is going on?

Also, I still go not understand why GMP was even used here for this simplify call, since everything is exact and symbolic.

@C_R 

         This time the system ran in optimized battery mode

Could you give instructions how to make Maple run in this mode? Never heard of this and googling does not show how to do it. Is this some option somewhere? I'd like to try it.

I run Maple now 2025 inside Linux which is installed inside virtual box.  

Or is this setting something done in the PC itself and not in Maple?  

I still do not understand what is going on. Why would running in "optimized battery" mode not make Maple hang on this call. Why would this make any difference in how Maple itself work?

@C_R 

great detective work. I assume this GMP is same as this https://gmplib.org/  The GNU
Multiple Precision Arithmetic Library

But why would simplify and Maple be using GMP here, since everything is symbolic and exact? 

look at parfrac in help pages

@janhardo 

Linear or non-linear odes:  is there difference for trying to get parameteric solution for both types of ode?

For linear ode's, parametric solution is not needed, since almost all such ode's can be solved directly (either explicit or implicit).

Only time to resort to parametric form of solution method is for non-linear ode's. Lets conside only first order for now. Parametric solution will have the form   

          y(x)=f(t,...)
          x(t)=g(t...)

In the above, "t" is the parameter. So we have two equations, and one parameter that holds them.

If we can eliminate the parameter "t", say using the eliminate command in Maple or most likely by solving for t as function of x from the second equation using RootOf and replace that in first equation, then we get explicit solution.

But most of the times this is not possible to do, or it can make the solution much more complicated. So in this case, some books leave the ode solution as above in parametric form. 

Also sometimes solving the ode parametric form can actually be simpler than using direct approach for nonlinear odes'. 

But the bottom line,  parametric solution is a way to make it possible to express solution of  nonlinear ode's where other direct method are not possible or produce much more complicated answers. 

Here is one example from the handbook of exact solutions

ode:=y(x)*diff(y(x),x)-y(x)=-6/25*x+2/25*A*(2*sqrt(x)+19*A+6*A^2/sqrt(x));

Book solution is

The parameter above is tau.  You see, the solution is easy to read (one line!) , but this is because it is parametric. Most such odes can be hard or not possible to rewrite as explicit or even implicit form. But possible as parametric. 

As far as I know, Maple dsolve have no option to obtain/ask for parametric solution, in the sense the above book gives. 

Maple solution for the above is below. You see it is more complicated (specially the explicit one) but on the other hand, it is not parametric, so no need to try to solve for the parameter

Download parametric_sol.mw

The above book has many such ode's I found which Maple 2025 dsolve can't solve, but book has solutions for in parametric form.