Help me, I want to make this system be stable on graphs? How to make this system stable in plot?

This is my model:

dx/dt=\[Alpha]*
  x[t]*(1 - (x[t]/n)) - ((\[Beta]*x[t]*
     y[t])/(1 + (\[CapitalTau]*\[Beta]*x[t]))) - (x[
    t]*\[CapitalEpsilon]);
dy/dt=y'[t] == -\[Gamma]*y[t];

Prove: If a is an irrational number, then the function y = cos (ax) + cos x is not periodic.
Is it possible to graphically represent or calculate this fact using an example?

I try to get some Bilinear form for some PDE equation  and already i have algorithm by writing in lecture but i can't apply i don't what is mistake i did, and i didn't seen some of this lecture code in maple  like (myint(expr,var))
 i  do upload PIcture of algorithm and example which they get Bilinear form 

Bilinear.mw

thanks for any help

I have a 2-parameters quartic equation in n (where n>=2 and integer) and want to find for which parameter values it is zero, if any exists.

Here I am analyzing the signs of each coefficient, but is there a faster way to solve my problem?
Thanks.

quartic_equation_in_n.mw

I am creating an algebra that includes shift operators. These operators commute with one another, but do not commute with anything else. I know that the Physics package enables you to make symbols non-commutative, but I would still like these operators to commute with one another. How can I do that?

Maple code example p.136 programming guide.

Explain the function of the word "divisible" in this maple code?

Why isn't divisible defined with an operator like -> ?

>L:= [seq( i, i=2..100)]:

> divisor := 2:

>while ( numelems( L ) > 0 )

do

divisible, L := selectremove( i->(i mod divisor = 0), L ):

n := numelems( divisible );

if ( n > 0 ) then

printf( "%d integer%s whose smallest prime divisor is %d\n",

n, `if`( n > 1, "s", "" ), divisor ):

end if;

divisor:=nextprime(divisor);

end do:

If a point is chosen in the Euclidean plane, then it is red or black.
It must be proven that there is then an equilateral triangle with corners of the same color.

dsolve gets stuck on a problem. Attached is the worksheet.

In Case I, dsolve solves the two ODEs separately. In Case II, dsolve solves them together, but only if I define a constant. In Case III the constant is not defined. dsolve never returns, and I have to hit the stop sign. The question I have: Is there a consistent method to the failure so that I can avoid the problem in the future with other ODEs?

dsolve_bug.mw

Question: Is there a style for the icons from the palettes? 

(The rest of this post is a screenshot because MaplePrimes can't show the change in fonts.)s a

How do I get alpha to display as the Greek letter in DataFrame Row column?

Download 2024-12-01_Q_Data_Table_alpha_as_Greek_Letter.mw

An oddly shaped Christmas package is a collection of centrally stacked cube-shaped boxes with ever smaller sides. From bottom to top, the edge lengths of the stacked cubes run like the sequence of the reciprocals of the sequence of the square roots of the natural numbers. How high is the package? How much paper is needed to wrap the package? What is the total volume enclosed by all the packages?

why i take intgral from equation it must apply for each term but just by sign is show up how it will work?

Download int.mw

I have a set of four equations along with specific parameter values provided in the dataset. I need to create a graph where I can dynamically adjust the values of parameters g2 and y within the specified range given in the sheet.
question_plot_slider.mw

Could you provide a maple code that allows for this flexibility, ideally with interactive controls (like the slider buttons shown in the example figure)

Hello,

I am working on a problem involving Newton's Law of Cooling in Maple, I want to:

1. Solve for the cooling constant k,
2. Find how long it takes for the pizza to cool to 300 F,

Here is the code I am currently using:

with(plots):

T__s := 75;  # Surrounding temperature
ode := diff(T(t), t) = k*(T(t) - T__s);

# General solution
general_solution := dsolve(ode, T(t));

# Initial condition: T(0) = 350
T := t -> 75 + exp(k*t)*c__1;
C := solve(350 = 75 + exp(0)*C__1, C__1);

# Solve for k using T(5) = 340
k := solve(340 = 75 + 275*exp(5*k), k);
k := evalf(k);

# Solve for time to reach T = 300
time_to_reach := solve(300 = 75 + 275*exp(k*t), t);
time_to_reach := evalf(time_to_reach);

# Define T(t) with solved constants
T := t -> 75 + 275*exp(k*t);

# Plot temperature over time
temp := plot(T, t = 0 .. 280, 75 .. 360, title = "Exponential Decay of Pizza Temperature", labels = ["t (minutes)", "T(t) (°F)"], color = blue);

# Plot T__s as a horizontal line
T__sur := plot(T__s, t = 0 .. 280, color = red, linestyle = dash);

# Combine and display plots
display([temp, T__sur]);

The code works, but I am wondering if there is a more efficient or genuine way.

I would greatly appreciate any advice or alternative approaches to solving and visualizing this in Maple.

Thank you in advance for your insights!

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With the latest version of Maple I get an indenting space when I click "Shift+Enter".
For example 

But I don't like it: suggestion? Thanks