A farmer has exactly 100m of wire mesh fence available to enclose a pasture. The fence must begin and end at his large oak tree. To do this, imagine the usual "north-south/west-east" cross of the cardinal directions in the drawing plane. The oak tree is at the center of this.

1. All land that lies west of the imaginary axis is not worth a cent.

2. All land that lies east of the oak tree becomes continuously more expensive the further it is from the north-south axis. The property value is based on the function y = k · x, where y represents the price per square meter and x represents the distance in meters to the north-south axis. k is a proportionality factor, which for the task is k = 1 euro/m^3.

a) On which curve must the fence run so that the enclosed pasture area has the greatest possible value?

b) On which curve must the fence run if instead of the distance x from the north-south axis the distance r from the oak tree is decisive with the same factor k?

I was watching Maple's video for conference 2024. In one of the presentation, this example is given

But in my Mapple 2024.2 I get an error typing the same command:

Download powerSeries_nov_14_2024.mw

Link to the video is here  it is around 39:00 in time. 

Any one knows why I get an error using same command shown in the video?

I tried connecting Maple to Jupyter Notebook, but it seems that it is not keen on outputting everything within the for loop; it only outputs the last item.

for i from 1 to 24 do
    print(i);
end do;

I've noticed that the Maple interface is always white, and after a long time, it causes eye strain. I wonder if it's possible to adjust the interface color, similar to Mathematica. My system is Windows 11.

Currently, I often use VSCode as an alternative, but some mathematical symbols don't display very clearly.

I have noticed similar discussions, such as this one, but I don’t know how to do it

In the attachment are three plotting issues that might be (partially) related.

 
Jagged shading     

Loss of color and incomplete clipping

The last one is the most severe because it takes color away when a plotobject is inside another object.

How can this be fixed? Explanations always welcome.

Shading_artefacs_and_lost_labels_and_color.mw

I have been working on solving a system of PDEs and plotting the results. However I've been encountered issues with setting the spacestep and timestep parameters.

First of all, i attempted to plot graphs t=0..2 using the animate command,

with spacestep = 5*10^-4 x 1/151,          timestep=1/1000

However, as shown in the image, an error ocurred indicating that calculations could not proceed after 1.57 sec.

Secondly, i kept the same spacestep but changed the timestep to 1/100 for plotting graphs 
t=0..2. This time, the graphs were plotted without any issues.

I initially beleved that larger spacesteps or timesteps would produce more accurate data. However, in my case, simply increasing these parameters did not work.

I would greatly appreciate if you could provide guidance on what factors should be considered when setting timestep and spacestep parameters, or any experiences in resolving similar issues.

Looks like this

From: dsolve_numeric_output_with_extra_brackets.mw

which was derived from a 2d document where I removed all unnecessary overhead.

When the option output=listprocedure is removed, this extra argument is not shown any more.

With that extra argument substitution of a solution into the corresponding ode(s) is not possible.

Any idea why that is? How to avoid or remove it?

What we are looking for is a flat polygon with N corners and side lengths 1,..., N, which has a maximum surface area.
BTW:
1.) I am a Maple newbie and would like to get to know the diversity and power of the Maple world. For this reason, I occasionally post tasks here from various areas of mathematics and of varying difficulty levels in order to learn from the answers. Of course, I know the solutions to these tasks. So these are not homework.
2.) I have difficulty subsequently inserting text at any point in working worksheets. I keep getting error messages because "or" or ";" is missing. What am I doing wrong?

Continuing from my previous post on "Exploring Oscillators: A Simple Pendulum Worksheet," we now dive deeper into the fascinating progression of oscillatory systems—from linear oscillations to complex, nonlinear dynamics with chaotic behaviors. This post examines how adjusting parameters in oscillatory models, such as the Duffing oscillator, reveal rich dynamics, including resonance and chaos.