How did Maple arrive at the following, implicit solution,

MSimplicitesolution := (-9*y(x)*(-y(x)*x^2)^(1/3)*6^(2/3)*x^2 + 16*_C1*x^(8/3) - 24*x^2 + 6)/(16*x^(8/3)) = 0, 

to the following 'ode',

ODE:= (2/3)*(int[(y'(x)*(x^2)/((x^2) -1)]) =int(-sqrt [2*y(x)])?

'odeadvisor' suggested y=G(x,y'(x), but I could not see how this could be implimented with this equation.

(Unfortunately, I am unable to download the Maple worksheet onto this sheet at this time.  Any assitance

would be appreciated.                

I want to write the expresstion x^3 + (-m - 1)*x^2 + (-4*m - 3)*x in the form x^3 - (m-1) x^2 - (4m + 3). I tried
collect(expand(x^3 + (-m - 1)*x^2 + (-4*m - 3)*x), x)

I get x^3 + (-m - 1)*x^2 + (-4*m - 3)*x

Why is Maple not calculating 'sqrt' and continuously showing 'Evaluating'?

Download q_sqrt.mw

Hi dear maple users
I have a BVP problem, how can get this problem solved?

Download ex.mw

Help me please?

ElzakiTransform := proc(f, t) int(f*exp(-t/v)*v, t = 0 .. infinity); end proc;
f := e^(n*t);
result := ElzakiTransform(f, t);
result;

Is this true?

For_MaplePrimes_question.mw

In the above Maple document, I present a puzzling problem:  When I use plot3d, the options

font = [Times, bold, 16], labels = ['u', 'v', 'z'], labelfont = [Times, bold, 40] in the command

with(plots);
plot3d([u*sin(2*v), u^2, u*cos(2*v)], transparency = 0.60, shading = none, font = [Times, bold, 16], labels = ['u', 'v', 'z'], labelfont = [Times, bold, 40], grid = [60, 60]);

produces nice big labels on the axes, which are visible as opposed to the almost invisible default size, especially on printouts but when I use these options as in below command:

fieldplot3d([0, 0, -y], x = -2 .. 2, y = -2 .. 2, z = -2 .. 2, arrows = `3-D`, fieldstrength = maximal(0.5), font = [Times, bold, 16], labels = ['x', 'y', 'z'], labelfont = [Times, bold, 40], grid = [4, 4, 4])

the lables x, y and z on the fieldplot are small, the default.  I used the same option and get different results.

I have been researching this for almost 2 hours and I can't find a way to increase the font size in the fieldplot command.

Is this a bug or does the fieldplot command not use these options the way it is used in the plot3d command?

Thank You for reading my question. (I am relatively inexperienced with Maple.)

Tom K.

I somehow managed to turn off autosave some time ago. Now I have reenabled it, but Maple still doesn't create any backups. Am I missing something?

Any help is appriciated.

There are various variants of graph coloring, such as when I want to compute the star chromatic number of a graph, Maple (or Mathematica) seems not to provide relevant functions.

Fortunately, the software ColPack   offers this functionality （Note: I just noticed that this software also uses greedy coloring instead of accuracy）. However, it supports the MTX format. So, the question is: 

•  How can I write a graph in MTX format?

And 

•  how can the MTX format be converted into a graph format?

Of course, I would like to perform these operations in Maple.  (SageMath may have something)

The following is an example (bcsstk01.mtx） in the directory `ColPack-master/Graphs directory` of the source code of ColPack.

bcsstk01.mtx.txt

./ColPack -f ../../Graphs/bcsstk01.mtx -m STAR
 Out: 11

But I do not know what the graph in the example is. On the contrary, I would like to compute the star chromatic number of the Petersen graph, and I also don't know how to convert it into the MTX format like the above.

with(GraphTheory):
with(SpecialGraphs):
P:=PetersenGraph()

I don't understand what the very long decimal numbers (like 2.8322685185200e+06) in the third column in the MTX-file. Will it affect the  imformation of the entire graph?

For MTX format, see https://math.nist.gov/MatrixMarket/formats.html.  For graphs, the numbers in the third column can all be considered as 1 (with the first two columns representing vertices, and their adjacency). Of course, this is my interpretation and may not necessarily be correct.

How to conver a patial differetial equation to ordinary differential equation with or without dchange?
 

Download pde_to_ode.mw

I make more and more use of the FunctionAdvisor. I have started to apply rules from the advisor to expressions. Here are two examples with questions:

Any advice?

Download Applying_identities_from_FunctionAdivisor.mw

Dear Users!

I hope everyone is fine here. I want to solve the following system of PDEs associated with Robin-type boundary conditions. But got the error. Kindly help me to fix this issue. Thanks

restart; TT := 0.1e-2; l := 1/5; b[1] := .18; b[2] := 2*10^(-9); k[1] := 1.3*10^(-7); k[-1] := 24; k[2] := 7.2; p := .9997; d[1] := 0.412e-1; f := .2988*10^8; g := 2.02*10^7; s := 1.36*10^4; E[0] := 3.3*10^5; T1[0] := .5*10^9; C1[0] := 3.3*10^5; alpha[0] := 10^(-10); D1 := 10^(-6); D2 := 10^(-2); D3 := 10^(-6); d[4] := 1.155*10^(-2); t[0] := 1/D1; kappa := 10^4; k[3] := 300*(24*60); chi := 0; sigma := d[1]*t[0]; rho := f*t[0]*C1[0]/(E[0]*T1[0]); mu := k[1]*t[0]*T1[0]; eta := g/T1[0]; epsilon := t[0]*C1[0]*(p*k[2]+k[-1])/E[0]; omega := D3/D1; beta1 := b[1]*t[0]; beta2 := b[2]*T1[0]; phi := k[1]*t[0]*E[0]; lambda := t[0]*C1[0]*(k[-1]+k[2]*(1-p))/T1[0]; psi := t[0]*(k[-1]+k[2]); gamma1 := chi*alpha[0]/D1; delta := D2/D1; kappa := k[3]*t[0]*C1[0]/alpha[0]; xi := d[4]*t[0]; PDE1 := diff(u(y, t), t) = diff(u(y, t), y, y)-gamma1*(u(y, t)*(diff(theta(y, t), y, y))+(diff(u(y, t), y))*(diff(theta(y, t), y)))+sigma*piecewise(y <= l, 0, 1)+rho*C(y, t)/(eta+T(y, t))-sigma*u(y, t)-mu*u(y, t)*T(y, t)+epsilon*C(y, t); PDE2 := diff(theta(y, t), t) = delta*(diff(theta(y, t), y, y))+kappa*C(y, t)-xi*theta(y, t); PDE3 := diff(T(y, t), t) = omega*(diff(T(y, t), y, y))+beta1*(1-beta2*T(y, t))*T(y, t)-phi*u(y, t)*T(y, t)+lambda*C(y, t); PDE4 := diff(C(y, t), t) = mu*u(y, t)*T(y, t)-psi*C(y, t); ICs := u(y, 0) = piecewise(0 <= y and y <= l, 0, 1-exp(-1000*(x-l)^2)), T(y, 0) = piecewise(0 <= y and y <= l, 1-exp(-1000*(x-l)^2), 0), C(y, 0) = piecewise(l-epsilon <= y and y <= l+epsilon, exp(-1000*(x-l)^2), 1-exp(-1000*(x-l)^2)), theta(y, 0) = 0; BCs := {(D[1](C))(0, t) = 0, (D[1](C))(1, t) = 0, (D[1](T))(0, t) = 0, (D[1](T))(1, t) = 0, (D[1](theta))(0, t) = 0, (D[1](theta))(1, t) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = 0};

PDE:= {PDE1, PDE2, PDE3, PDE4}; pds := pdsolve(PDE, {ICs}, BCs, numeric, spacestep = 1/100, timestep = 1/100);

Error, (in pdsolve/numeric/process_PDEs) specified dependent variable(s) {(D[1](C))(0, t) = 0, (D[1](C))(1, t) = 0, (D[1](T))(0, t) = 0, (D[1](T))(1, t) = 0, (D[1](theta))(0, t) = 0, (D[1](theta))(1, t) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = 0} not present in input PDE
 

Good afternoon, I'm trying to simplify or that Maple gives me the factor of (3a - 3) and it doesn't. The result that should be thrown is 3(a-1).

Hi.

When trying to open my document it says:
''There were problems during the loading process, Your worksheet may become incomplete.''

Would you mind helping me?
I saw some scripts on how to fix it, but simply can't solve it myself.

Regards Samuel

Basismat_2_noter.mw

Hello do u know how to make this code more optimal? this is very long time to plot.

g := evalf((Beta(1/4, 1/4)/2)^4);

A := Pi*r*cos(theta) - Re(WeierstrassZeta(r*exp(theta*I), g, 0) + Pi*WeierstrassPPrime(r*exp(theta*I), g, 0)/g);
B := Pi*r*sin(theta) + Im(WeierstrassZeta(r*exp(theta*I), g, 0) - Pi*WeierstrassPPrime(r*exp(theta*I), g, 0)/g);
C := sqrt(6*Pi/g)*Re(WeierstrassP(r*exp(theta*I), g, 0));

plot3d([A, B, C], r = 1/5 .. 4/5, theta = -Pi .. Pi, view = [-8 .. 8, -8 .. 8, -8 .. 8], shading = zhue, grid = [200, 200]);

Good day everyone.

I am trying to write a code with variable stepsize involving tolerance. two vectors are declare for the errors. However, I don't know how to declare the two errors in comparison with the tolerance. Please kindly help. Also, any other modification to the entire code is also welcomed. Thank you all and best regards.

The code is as attached.

Variable_step_size_Falkner.mw