In the attached file, I would like to evaluate the integral according to (16) and the minimum according to (17). I would appreciate your help. The goal is to calculate the coefficients a and b.

Euler_eq.mw

In the attached file test1, two terms are to be compared using the "is" function. Theoretically, these terms are equal. A plot is provided for illustration. However, regardless of which symbol ("equal," "not equal," etc.) is used in "is," the result is always "false." What am I doing wrong?

Download test1.mw

According to the help text in Maple 2024.2, a number of classical integral equations can be solved using "intsolve". The Volterra equation of the first kind, with an upper limit of integration x, is of particular interest. A long time ago, I had to solve a similar equation. This one arose from a model of a real-world process, but instead of x, the upper limit of integration was the function y(x), which I had to calculate. I painstakingly solved it to a good approximation. Is there an algorithm in Maple that can at least calculate an approximate solution, or is a numerical solution, e.g., using Ritz, the only option?

edited: I forgot to upload an example

 test.mw

On my journey of discovery through the Maple world, I now want to try out Maple's convenient features in the complex plane, something that used to be laboriously worked out and demonstrated on the blackboard with chalk. I couldn't find a suitable introduction in the help text. I'm interested in whether a package needs to be loaded and how to handle polynomials, series, and line integrals (I have a reasonable understanding only of the theory).

In the attached file, I want to calculate the integral Q1. Numerically, this is easy to do in Maple. For theoretical reasons, the exact result pi/e is known. However, a contradiction arises between command lines (4) and (5). Command (6) is also unsuccessful, as its exact result is unknown. What am I doing wrong?

Download test.mw