I am currently working with inert integrals and summations in Maple, and I encountered a difficulty when manipulating symbolic expressions. I would appreciate any suggestions or recommended approaches.

Specifically, I would like to achieve the following:

1. Convert an inert expression in the form of a “summation inside an integral” into an equivalent “sum of integrals” form.
   In other words, transform expressions of the type:
   Int(i=1∑n​fi​(x,t),x=a..b)

   into
   ∑​Int(fi​(x,t),x=a..b)

   while preserving the inert (Int) representation rather than evaluating the integral directly.

   I have tried commands such as value, expand, convert, and related manipulation methods, but I have not yet found a suitable solution.
    

2. The integrand contains two variables, where xxx is the integration variable.
   How can terms that are independent of xxx be automatically extracted outside the inert integral? For example, if the integrand contains coefficients or functions depending only on ttt, I would like Maple to rewrite
   Int(g(t)f(x),x=a..b)

   as g(t)Int(f(x),x=a..b)

   without forcing evaluation of the inert integral.

   Any recommendations, built-in commands, or pattern-based approaches would be greatly appreciated.
   question525.mw

In my Maple program, the voltage output of the system is computed as a time-domain response under different time intervals. The response curve has already been successfully obtained and plotted.

However, I would like to further extract and plot the envelope of this response. I initially attempted to determine the envelope by identifying the extrema of the signal, i.e., by solving the condition that the time derivative of the response equals zero. Unfortunately, this approach consistently leads to error messages, and I am not sure whether the issue is related to symbolic differentiation, numerical noise, or the implementation itself.

Could anyone please advise on:

1. The correct way to extract an envelope curve from a time-domain signal in Maple?

2. Whether there are alternative or more robust methods (e.g., based on numerical post-processing, signal processing techniques, or built-in Maple tools) to obtain the envelope, especially for numerically computed responses?

Any suggestions or example commands would be greatly appreciated.

Thank you in advance for your help.
numsolve-1229.mw

I would like to keep writing commands on the same line without automatically creating a new line break. Is there a way to achieve this in Maple?

I'm working on a system of coupled ordinary differential equations with multiple degrees of freedom. I would like to explore the existence of multiple solutions by using a bifurcation diagram. To this end, I tried using the built-in Bifurcation command in Maple. However, the command repeatedly returns errors and fails to produce the expected plots.

Has anyone successfully used the Bifurcation command in Maple for coupled ODE systems? Are there specific settings or prerequisites that I might be missing? I would greatly appreciate any guidance or example code demonstrating how to properly use this command for such systems.
bifurcation.mw