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there is any way to use explicate for remove the n...

Asked by: salim-barzani 1560
pde explicit differential-equations
February 28 2025
1  2

I want to remove the Lambert function (LambertW) from my equation, but I don't know how. I tried using the explicit option, but it didn't work. How can I express the equation without LambertW?

> 

restart
> 

with(PDEtools)
> 

with(LinearAlgebra)
> 

NULL
> 

with(SolveTools)
> 

undeclare(prime)

`There is no more prime differentiation variable; all derivatives will be displayed as indexed functions`

 (1)
> 

declare(u(x, y, z, t))

u(x, y, z, t)*`will now be displayed as`*u

 (2)
> 

declare(f(x, y, z, t))

f(x, y, z, t)*`will now be displayed as`*f

 (3)
> 

pde := diff(diff(u(x, y, z, t), t)+6*u(x, y, z, t)*(diff(u(x, y, z, t), x))+diff(u(x, y, z, t), `$`(x, 3)), x)-lambda*(diff(u(x, y, z, t), `$`(y, 2)))+diff(alpha*(diff(u(x, y, z, t), x))+beta*(diff(u(x, y, z, t), y))+gamma*(diff(u(x, y, z, t), z)), x)

diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

 (4)
> 

pde_nonlinear, pde_linear := selectremove(proc (term) options operator, arrow; not has((eval(term, u(x, y, t) = a*u(x, y, t)))/a, a) end proc, expand(pde))

0, diff(diff(u(x, y, z, t), t), x)+6*(diff(u(x, y, z, t), x))^2+6*u(x, y, z, t)*(diff(diff(u(x, y, z, t), x), x))+diff(diff(diff(diff(u(x, y, z, t), x), x), x), x)-lambda*(diff(diff(u(x, y, z, t), y), y))+alpha*(diff(diff(u(x, y, z, t), x), x))+beta*(diff(diff(u(x, y, z, t), x), y))+gamma*(diff(diff(u(x, y, z, t), x), z))

 (5)
> 

thetai := t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]; eval(pde_linear, u(x, y, z, t) = exp(thetai)); eq15 := isolate(%, w[i])

t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]

  

w[i]*k[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+12*k[i]^2*(exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i]))^2+k[i]^4*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])-lambda*l[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+alpha*k[i]^2*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+beta*k[i]*l[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])+gamma*k[i]*r[i]*exp(t*w[i]+x*k[i]+y*l[i]+z*r[i]+eta[i])

  

w[i] = -(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

 (6)
> 

sol := solve(eq15, w[i], explicit)

-(t*k[i]^4+gamma*t*k[i]*r[i]+alpha*t*k[i]^2+beta*t*k[i]*l[i]-lambda*t*l[i]^2+LambertW(12*t*k[i]*exp(-(t*k[i]^4+alpha*t*k[i]^2+beta*t*k[i]*l[i]+gamma*t*k[i]*r[i]-lambda*t*l[i]^2-x*k[i]^2-y*k[i]*l[i]-z*k[i]*r[i]-eta[i]*k[i])/k[i]))*k[i])/(t*k[i])

 (7)
 

NULL

Download remove.mw

How to find real dimension of the solution set for...

Asked by: bcp 5
polynomial dimension regularchains
February 28 2025
1  0

I have a system of polynomial equations where the unknowns are real numbers. The set of solutions is infinite (positive-dimensional). How can I compute the real dimension of the solution set (i.e. of a real algebraic variety)?

As it as mentioned in arXiv:2105.10255, this can be done using the RealTriangularize function from the RegularChains package. What is best way of getting the real dimension from the regular_semi_algebraic_system object, which is returned by this function?

question about registering for Maple 2025 webinar...

Asked by: nm 11353
February 28 2025
2  1

I got email to register to "see" Maple 2025 :

for a special advanced look at Maple 2025

But I do not understand what does registering here means. Do I then get a link to some Maple internal URL to watch Video at that time? It says

Date/Time: Tuesday, March 18, 2025 at 11:00 AM
Language: English
Duration: 1 hour

If I register, then what happens?  do I get a link that opens at the time time to watch it? If so, why does one have to register to watch a Maple video? Why is the link not made public for any one to watch? Does one have to be at the browser at that exact time for the link to open?

I just do not know what a Maple webinar means.  Is it like a youtube video?

3D animation/projection...

Asked by: Shashikant Sharma 25
February 27 2025
3  10

Hi,

Would someone please help me with how to achieve this cool animation shown here.

3d plot

How add lebel into inside graph ...

Asked by: Arya-S-AA 175
contourplot textplot plotting
February 27 2025
1  19

How i can add lebel inside graph  like this picture for some graph , in somecoding i have but i can't how it work i want add to  my code but i can't do the same as paper did

label.mw

how to find most compact representation of matrix ...

Asked by: MichalKvasnicka 219
matrix exponential
February 26 2025
1  9

I am trying to find the most compact form of the symbolic matrix exponential of the specific 4x4 input matrix with the following form:

where all variables are non-negative real constants, with the additional problem specific conditions:

1. omega__1 + omega__2 = 1 

2. f__p + f__d1 + f__d2 = 1

There are many mathematically identical subterms at the matrix exponential, so I would like to use a few proper substitute subexpressions, but Maple does not apply it, without any error or warning message.

Moreover, I have no idea how to incorporate above-mentioned additional conditions into the simplification process.

expFT_compact.mw

I will be very happy for any help with this problem.

Michal

Calculate the following Riemann integral...

Asked by: Alfred_F 330
integration limit
February 26 2025
1  3

I am very interested in problems of integration and limit determination. In order to be able to continue other work with the help of Maple, I would like some advice on solving the following problem. The solution I know of using pen and paper is very tiring, perhaps Maple can make it easier:

To calculate Int(from 0 to 1)[ln(x)*ln(1-x)]dx
or, for obvious reasons, formulated differently:
Let eps, delta>0. Calculate
lim(eps, delta-->0)Int(0+eps to 1-delta)[ln(x)*ln(1-x)]dx

how to include subscripts in text command...

Asked by: pmdearing 15
subscript plotting incomplete-question
February 25 2025
2  1

Is there a good way to include subscript(s) to a letter within a 'text' command?  Currently I do this by specifying the coordinates, letter, and font for the letter, then specify the coordinates, number and font for the subscript.  However, with this method the letter and subscript can be compressed if the viewing interval is compressed or expanded.  

Is there another way to include letters with a subscript in a text command?

How to use 'view' to specify the interval of the d...

Asked by: Aixleft math 120
implicitplot view plotting
February 25 2025
2  4

Hi! A basic issue.

Why view=[-2 ..1, -2 ..5]  is not useful here? According to the output, only the green line meets the view settings. I want to extend the left side of these three lines appropriately (show the intersection)

> 

with(plots)
> 

l := 2*x+y+1 = 0; l1 := 4*x+2*y+2 = 0; l2 := 4*x+2*y-2 = 0; l3 := 4*x-2*y+6 = 0

2*x+y+1 = 0

  

4*x+2*y+2 = 0

  

4*x+2*y-2 = 0

  

4*x-2*y+6 = 0

 (1)
> 

 

> 

display({implicitplot(l, color = black, legend = l, thickness = 5, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l1, color = red, legend = l1, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l2, color = blue, legend = l2, view = [-2 .. 1, -2 .. 5])}, {implicitplot(l3, color = green, legend = l3, view = [-2 .. 1, -2 .. 5])})

 
 

NULL

Download The_intersection_parallelism_and_coincidence_of_two_straight_lines.mw

does remove_RootOf command affect the result?...

Asked by: ashy 35
rootof incomplete-question
February 25 2025
2  1

I have an epidemic model and the endemik equilibrium point contains rootOf _Z, here's one of the example

i still don't understand about the _Z and find the "remove_RootOf" command. Does it affect the result or is it an explicit result of Z?

Explore command to examine the effect of mu and si...

Asked by: jalal 435
explore densityplot plotting
February 25 2025
0  3

Hi,

I'm trying to use the Explore command to examine the effect of two parameters (mu and sigma) on the density function curve. The visualization isn't very optimal, especially with the mu parameter, and it's difficult to add options (range, color, gridlines, etc.). Any suggestions to optimize this idea? Thanks for your insights!

Q_Explore.mw

How solve ODE equation by specific method?...

Asked by: Arya-S-AA 175
ode syntax step-by-step
February 25 2025
3  6

when we have ode equation we say what is type of equation then  i want solve by this method say the name of method and if possible i want to solve this equation by the method step by step too, maple can do that? also can we plot the solution or any geometricall presentation , also i have error in writing exact form of equation

> 

restart
> 

"with(Student[ODEs]): "
> 

with(DETools)
> 

ode1 := diff(y(x), x)+2*x*y(x) = x

diff(y(x), x)+2*x*y(x) = x

 (1)
> 

Type(ode1)

{linear, separable}

 (2)
> 

W := dsolve(ode1)

y(x) = 1/2+exp(-x^2)*c__1

 (3)
> 

odetest(W, ode1)

0

 (4)
> 

ODESteps(ode1)

"[[,,"Let's solve"],[,,(ⅆ)/(ⅆx) y(x)+2 x y(x)=x],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Separate variables"],[,,((ⅆ)/(ⅆx) y(x))/(2 y(x)-1)=-x],["•",,"Integrate both sides with respect to" x],[,,∫((ⅆ)/(ⅆx) y(x))/(2 y(x)-1) ⅆx=∫-x ⅆx+`c__1`],["•",,"Evaluate integral"],[,,(ln(2 y(x)-1))/2=-(x^2)/2+`c__1`],["•",,"Solve for" y(x)],[,,y(x)=((e)^(-x^2+2 `c__1`))/2+1/2]]"

 (5)
> 

ode2 := (sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

(sin(x)*tan(x)+1)*dx-cos(x)*sec(y(x))^2*dy = 0

 (6)
> 

Type(ode2)

Error, (in Student:-ODEs:-Type) could not determine the solving variable. Please specify it as an extra argument in the form: y(x)

  
 

NULL

Download ode-example.mw

How can change the shape of plot in contour by usi...

Asked by: SSMB 100
explore plotting duplicate-question
February 24 2025
1  7

i want try all number to my parameter for check the shape of plot there is any way for doing that?

> 

restart
> 

with(plots)
> 

M := 4*b^2*beta*((a*y-2*alpha*t+x)*b^2+a*(-2*beta*t+a*(a*y-2*alpha*t+x)))/(-b^6*beta*y^2+(-4*t*y*beta^2+(-2*a^2*y^2+(4*(alpha*t-(1/2)*x))*y*a-4*(alpha*t-(1/2)*x)^2)*beta+3*a)*b^4+(-4*t^2*beta^3+4*a*t*(a*y-2*alpha*t+x)*beta^2-a^2*(a*y-2*alpha*t+x)^2*beta+6*a^3)*b^2+3*a^5)
> 

alpha = 1; beta := 1; a := -1; b := -2; t := 0

alpha = 1

  

1

  

-1

  

-2

  

0

 (1)
> 

plots:-contourplot(M, x = -100 .. 100, y = -100 .. 100, title = contour, grid = [100, 100], colorbar = false)

 
 

NULL

Download control-trajectory.mw

quick design question regarding my animation...

Asked by: jalal 435
February 24 2025
0  1

Hi,

just a quick design question regarding my animation. The color "AliceBlue" disappears from my background... Could it be a background option issue?

Q_AlceBlue_background.mw

bug report: Maple dsolve throws internal error on ...

Asked by: nm 11353
ode dsolve differential-equations
February 24 2025
3  4

THis IC for Abel ode is not valid and should result in no solution. But instead of returning NULL, dsolve throws internal error called Error, (in dsolve) invalid limiting point

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.2, Windows 10, October 29 2024 Build ID 1872373`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1844 and is the same as the version installed in this computer, created 2025, January 25, 22:5 hours Pacific Time.`

> 

ode:=diff(y(x),x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0;

diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0

> 

DEtools:-odeadvisor(ode);
sol:=dsolve([ode,y(1)=1])

[_Abel]

Error, (in dsolve) invalid limiting point

> 

tracelast;

 dsolve called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], arbitraryconstants = subscripted, atomizenames = true, build = false, numeric = false, type = none
 #(dsolve,80): error

 \`dsolve/IC\` called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = particular and general
 #(\`dsolve/IC\`,64): draft := procname(_passed,':-usesolutions = "general"');

 \`dsolve/IC\` called with arguments: [diff(y(x), x)-x^a*y(x)^3+3*y(x)^2-x^(-a)*y(x)-x^(-2*a)+a*x^(-a-1) = 0, y(1) = 1], {y(x)}, skipimplicit = false, skippparticularsolforlinearODEs = true, solution = {}, usesolutions = general
 #(\`dsolve/IC\`,277): zz := map(op,{\`dsolve/IC/_C\`({ANS[i]},funcs,x,ics)});

 \`dsolve/IC/_C\` called with arguments: {y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a)}, {y(x)}, x, [y(1) = 1]
 #(\`dsolve/IC/_C\`,1): ans := \`dsolve/IC/_C/do\`(solns,depvars,t,inits,'evaluated_ans', "default",':-giveup = giveup');

 \`dsolve/IC/_C/do\` called with arguments: {y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a)}, {y(x)}, x, [y(1) = 1], evaluated_ans, default, giveup = giveup, usecansolve = false
 #(\`dsolve/IC/_C/do\`,133): Solns := map((u, S) -> map(limit,S,op(u)),csol,Solns);

 limit called with arguments: y(x) = -exp(2*x^(-a+1)/(a-1))/(_C[1]-2*2^(2*(a+1)/(a-1))*(1/(-a+1))^((a+1)/(a-1))*(2^(-(5*a-3)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*(-4*x^(-a+1)*a^2/(-a+1)+8*a*x^(-a+1)/(-a+1)-4*x^(-a+1)/(-a+1)+2*a-2)*WhittakerM(-(a+1)/(a-1)+1/(a-1), -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a))-2^(-(3*a-1)/(a-1))*(1/(-a+1))^(-(a+1)/(a-1))*x^(2*a)*WhittakerM(-(a+1)/(a-1)+1/(a-1)+1, -1/(a-1)+1/2, 4*x^(-a+1)/(-a+1))*(-a+1)^2*(x^(-a+1)/(-a+1))^(1/(a-1))*exp(-2*x^(-a+1)/(-a+1))/((a+1)*(-3+a)))/(-a+1))^(1/2)+x^(-a), _C[1] = exp((4*I)*Im(1/(a-1)))*infinity, parametric = false
 #(limit,2): return map(thisproc,_passed)

 limit called with arguments: y(x), _C[1] = exp((4*I)*Im(1/(a-1)))*infinity, parametric = false
 #(limit,33): error "invalid limiting point"

Error, (in dsolve) invalid limiting point

 locals defined as: ddir = ddir, dexpr = y(x), fexpr = fexpr, r = r, x = _C[1], fL = fL, L = exp((4*I)*Im(1/(a-1)))*infinity, efloat = efloat, lfloat = lfloat, ind_dexpr = ind_dexpr, ind_L = ind_L, lexpr = lexpr, t = t, limr = limr, liml = liml, pt = (_C[1] = exp((4*I)*Im(1/(a-1)))*infinity), inertfunctions = {}, limitX = limitX, parameters = parameters, Y = Y, limc = limc, cexpr = cexpr, texpr = texpr, bexpr = bexpr, limt = limt, limb = limb, param = param, c = c, N = N, Z = Z, P = P, o = o, e = e, uneval = uneval, i = i, A = A, cond = cond, ll = ll, rr = rr

> 

 


 

Download internal_error_instead_of_no_solution.mw

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