The_Bohrs_Model_-_MaplePrimes.mw

Look at the equation (11) in the Maple's document. I would like to force Maple to let the variable "r" inside the squared root so to get the equation (12). Any idea of doing that?  Thank you in advance for your help.

Already  by Help of my favorite Dr.David he did find the thus three step for non schrodinger equation but in here i got some issue of coding which is so different from before, is about transformation of pdes to two parts od real and imaginary part and then substitution our function the functions is clear but combining them and findinf leading exponent and resonance point and finding function in step 3 in different and jsut the function is different with eperate the real and imaginary part for finding step one ...

note:=q=u*exp(#) then |q|=u

schrodinger-test.mw

paper-1

paper-2

(2500iw/(1+5iw) )+(200iw/1-10iw)+5 rationalize and simplify

Hello All

I have the system of 4 differential equations with retarted delay (t-tau) and advanced argument (t+tau). The problem is also considered as a two-value boundary problem since some variables have initial conditions and some have terminal ones.

Here is a model:

Data:

A := 10;
B := 5;
C := 2;
tau = 0.5;
T := 10;
 z := 5;
 N := 20;
 

System:

sys := diff(K(t), t) = A*Q(t - tau) + K(t), diff(Q(t), t) = l_Q(t)*z - N, diff(l_K(t), t) = B*Q(t - tau) + l_K(t), diff(l_Q(t), t) = l_K(t + tau)*K(t + tau) + C;

Initial and terminal conditions:
 
inc := K(0) = 50, Q(0) = 200, l_K(T) = -20, l_Q(T) = 0;
   

I will appreciate any direction/suggestion on how this system can be solved. 

Dmitry

I was surprised that Maple can't solve this first order ode which is exact ode.

I solved by hand and Maple says my solution is correct.

Any one can find why Maple failed to solve this and if older versions can solve it? Also tried implicit option, but that did not help.

Download maple_solving_exact_ode_august_25_2025.mw

In the attached file, the trigonometric term (2, term) is transformed into a term (3, term1) consisting of radicals. Is there a Maple procedure that can be used to reverse this process? Given an algebraic term (e.g., consisting of radicals, powers, etc.), under what conditions can it be transformed into a trigonometric form (not a Fourier series) in the sense of (3) according to (2)?test.mw

Download test.mw

As we can see, RealDomain:-solve gives an incorrect solution to the following system: 

Download solve_returns_an_unsatisfiable_real_solution.mw

This appears to be a bug; is it possible to fix it? 
Text: 

sys := diff~(sqrt(2*a^2 - 8*a + 10) + sqrt(b^2 - 6*b + 10) + sqrt(2*a^2 - 2*a*b + b^2), [a, b]):
RealDomain:-solve(sys =~ 0, {a, b});

THis is problem from textbook. Maple do not give solution. 

But when asked for implicit solution, it gives one.  Should it not have done this automatically?

Download why_no_solution_maple_2025_1.mw

We see now there are two solutions for y(x), since quadratic.

So why dsolve do not solve this and at least give implicit solution automatically? Should this be reported as defect?

is been a while i work on a test still i am study and there is a lot paper remain and is so important in PDEs, a lot paper explain in 2003 untill know and there is other way to find it too but i choose a easy one but is 2025 paper  which is explanation is so beeter than other paper, also some people write a package for take out this test with a second but maybe is not work for all i  search for that  but i didn't find it i will ask the question how we can find thus as shown in graph i did my train but need a little help while i am collect more information and style of solving 

Download p1.mw

Hello everyone,
I hope this message finds you well. I am trying to plot a function f(x, y) and overlay its contour on a quarter ellipse using Maple 2015. However, I’ve encountered some difficulties and have not been successful so far. I would greatly appreciate any assistance in resolving this issue. Thank you!

Plotting in 2D

restart:with(plots):  aa := 4: bb := 2:  
f := -((x^(2))/(aa^(2))+(y^(2))/(bb^(2))-1)*((aa^(2)*bb^(2))/(aa^(2)+bb^(2))):  
plot3d(f,x = 0 .. aa/(2),y = 0 .. bb/(2),region = (x, y) -> ((2 x)/(aa))^(2) + ((2 y)/(bb))^(2)<= 1,axes = boxed,style = patchcontour, grid = [50, 50],orientation = [-120, 45],shading = zhue,title = "f(x,y) over quarter ellipse domain");

Contour plotting
xrange := 0 .. aa/(2): yrange := 0 .. bb/(2):  
nx := 100:   ny := 100:  
dx := (rhs(xrange) - lhs(xrange))/(nx-1):dy := (rhs(yrange) - lhs(yrange))/(ny-1):  
Z := Matrix(nx, ny, (i, j) -> local x, y, inside;x := lhs(xrange) + (i-1)*dx;y := lhs(yrange) + (j-1)*dy;inside := (((2 x)/aa)^2 + ((2 y)/bb)^2 <= 1);if inside then f(x, y) else NULL end if):  
contourplot(Z, xrange, yrange,contours = 15, filled = true, coloring = [blue, green, yellow, red], axes = boxed, title = "Contour plot over quarter ellipse", grid = [nx, ny]);  

Hi,
I would like to solve a system of 2 PDE with this code, but it does not work.
lin_eqs := {diff(h(x, t), t) + H*diff(u(x, t), x) = 0, diff(u(x, t), t) + g*diff(h(x, t), x) = 0};
sol := pdsolve(lin_eqs);
print('sol', sol);

Can you help me?Thanks
Best regards

Any idea why Maple simplifies 1+sin(x)^2 to 2-cos(x)^2?  Leaf count is larger also.

Download strange_simplification_august_20_2025.mw

Attached worksheet

Download internal_error_on_int_august_20_2025_maple_2025_1.mw

Update

fyi, Here is yet another int() error Error, (in type/trig) too many levels of recursion in Maple 2025.1. (also reported to Maplesoft).

Download another_int_error_too_many_levels_maple_2025_1.mw

Greetings

I trust that everyone is well here. I have an inquiry regarding the partitioning of a matrix BA, defined on both regular and irregular domains, into three matrices: Ad, Ab, and Ae, such that NewBA = Ad + Ab + Ae. Here, Ad comprises the entries of BA that reside within the domain, Ab includes the elements of BA located on the boundary, and Ae is derived as BA - Ad - Ab for any values of Mx and My. The specifics of matrix BA are contained in the attached document where NewBA constructed manually for different values of Mx and My for better understanding.
Splitting_a_matrix.mw
The attached file contains the matrix BA constructed in a square format. How may the BA matrix be adapted to create an irregular shape, such as a quarter circle?

The red dots indicate the mesh within the domain Ad, while the meshing along the blue line should occur in Ab.

I await your kind reply. Kindly ensure your well-being

I’m getting an error while solving the equations derived from the KKT conditions.
What syntax modifications should I make?
The decision variables are p1 and pr, with two constraints.

sheet: Q1_solve_equation.mw