MaplePrimes Questions

according to what is new in Maple 2025, it says

  • Maple 2025 introduces several important improvements to simplify regarding expressions containing exponential, trigonometric, hyperbolic, and/or inverse trigonometric functions, resulting in more compact results. Other commands in the math library also provide simpler results due to these improvements.

But I still see weakness in simplify. (see also recent question).

Here is an example, A and B below are equivalent mathematically. But A is almost twice as big. So one would expect simplify(A) to return B. right? But it does not. Also using size option has no effect.  

Does one need more tricks in Maple to make it simplify this? Is this not something that a powerful CAS software like Maple should have been able to do?

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`


A:=(-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4;
B:=(4*exp(x/2)-x-2)^2;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(4*exp((1/2)*x)-x-2)^2

#check leaf size
MmaTranslator:-Mma:-LeafCount(A);

22

MmaTranslator:-Mma:-LeafCount(B);

13

#check they are the same
simplify(A-B);

0

#then why Maple can not simplify A to B ??
simplify(A);
simplify(A,size);
simplify(A,size,exp);
simplify(A) assuming real;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

Student:-Precalculus:-CompleteSquare(A)

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

 

 

Download why_can_not_simplify_may_4_2025.mw

Using another software, all what is needed is call to Simpify to do it:

I also tried my most power full_simplify() function in Maple, and it had no effect

full_simplify:=proc(e::anything)
   local result::list;
   local f:=proc(a,b)
      RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
   end proc;

   #add more methods as needed

   result:=[simplify(e),
            simplify(e,size),
            simplify(combine(e)),
            simplify(combine(e),size),
            radnormal(evala( combine(e) )),
            simplify(evala( combine(e) )),
            evala(radnormal( combine(e) )),
            simplify(radnormal( combine(e) )),
            evala(factor(e)),
            simplify(e,ln),
            simplify(e,power),
            simplify(e,RootOf),
            simplify(e,sqrt),
            simplify(e,trig),
            simplify(convert(e,trig)),
            simplify(convert(e,exp)),
            combine(e)
   ];   
   RETURN( sort(result,f)[1]);   

end proc:

Calling full_simplify(A) did not simplify it.

I wanted to search for all files with some extention in directory tree. But when adding depth=infinity and also adding 'select'="*.log" (or whatever the extension I want is), then it returns an empty list even though there are files with this extension but deep in the tree.

If I remove select, then it does work, but it returns list of the files in the tree. Which I do not want. I want to filter these by select.

If I remove depth=infinity then select works but only finds such files at top level of the directory and does look down the tree where there are more such files.

It seems select and depth conflict with each others.  Adding 'all' option makes no difference.

I do not remember now if I reported this before or not.

Here is worksheet showing this problem

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

folder_name:="/home/me/maple2025"; #fails to find all such files
FileTools:-ListDirectory(folder_name,'select'="*.wav",depth=infinity);

"/home/me/maple2025"

[]

folder_name:="/home/me/maple2025"; #works but only top level
FileTools:-ListDirectory(folder_name,'select'="*.log");

"/home/me/maple2025"

["Maple_2025_Install_2025_04_03_12_34_10.log"]

folder_name:="/home/me/maple2025"; #works but this finds everything
FileTools:-ListDirectory(folder_name,depth=infinity);

"/home/me/maple2025"

`[Length of output exceeds limit of 10000]`

 


 

Download listdirectory_may_3_2025.mw

How can one get list of files with specific extension in the whole tree? And why is adding select makes it not work? Help does not say anything about select does not work when adding depth=infinity.

I suppose I can get list of all files in tree, then iterate over the list and remove all entries that do not end with the extension I wanted. But this is what select is supposed to do. For example

folder_name:="/home/me/maple2025/"; #works but this finds everything
L:=FileTools:-ListDirectory(folder_name,depth=infinity):
map(X->`if`(FileTools:-Extension(X)="wav",X,NULL),L);

Gives list of only files with extension "wav". So the above is workaround for now.

I’m currently trying to collect terms in an expression f^G(xi), but the result is not behaving as expected. I attempted two different coding approaches, but both resulted in errors. This particular case of collecting terms seems to be different from what I’ve encountered before, and I’m unsure how to resolve it.

Could you please advise on how to properly collect the terms in this situation and avoid the errors? Any insight into why this case behaves differently would also be appreciated.

Thank you for your help.

collect_term.mw

I am currently working with an ordinary differential equation (ODE) that I find difficult to express and solve accurately. In this ODE, the symbol f represents an exponential function rather than a typical variable, which adds to the confusion. Although I have followed the format used in related research papers, the results I obtain are not satisfactory.

Since this type of ODE is new and somewhat unfamiliar to me, I would greatly appreciate your guidance in:

  1. Properly formulating the ODE.

  2. Understanding the role of f in the context of exponential functions.

  3. Finding the correct and complete solutions.

  4. Learning how to clearly present each solution step by step.

Thank you in advance for your support.

AA.mw

These are the same (i.e. mathematically equivalent for real x)

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

But can't see how to use Maple to show this, other than numerically and by plotting.

Any one knows of a trick? Below is worksheet. Using another software, it was able to show they are same:

Here are my attempts in Maple 2025
 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

-x*(x-4*exp((1/2)*x)+2)

x*((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)

plots:-display(Array([plot(A,x=-3..3),plot(B,x=-3..3)]))

 

 

Digits:=16;
seq(MmaTranslator:-Mma:-Chop(A-B),x=-2..2,.1)

16

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

simplify(A-B);

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evala(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(normal(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B,exp) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evalc(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

 

 

Download show_same_may_3_2025.mw

Manually factoring each equation in this system one by one is time-consuming and inefficient. Is there a way to automate the factoring of expressions into two multiplicative terms—some of which may be single-term factors—using code?

restart

with(PDEtools)

NULL

with(SolveTools)

undeclare(prime)

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

(1)

G1 := 5*lambda^2*alpha[1]^4*alpha[0]*a[4]+lambda^2*alpha[1]^4*a[3]-10*lambda*alpha[1]^2*alpha[0]^3*a[4]+lambda*k^2*a[1]*alpha[1]^2-6*lambda*alpha[1]^2*alpha[0]^2*a[3]+alpha[0]^5*a[4]-k^2*a[1]*alpha[0]^2-3*lambda*alpha[1]^2*alpha[0]*a[2]+alpha[0]^4*a[3]+lambda*w*alpha[1]^2+alpha[0]^3*a[2]-w*alpha[0]^2+((lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1])*(diff(G(xi), xi))+lambda^2*beta[0]*a[5]*alpha[1]^2-4*mu*lambda*alpha[1]^4*a[3]+5*lambda^2*beta[0]*alpha[1]^4*a[4]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]+12*mu*alpha[1]^2*alpha[0]^2*a[3]+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*lambda*alpha[1]^2*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*lambda*alpha[1]^2*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3]-2*w*alpha[0]*beta[0]+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*mu*w*alpha[1]^2)/G(xi)+((1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]+6*mu*beta[0]*alpha[1]^2*a[2]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]+3*beta[0]^2*alpha[0]*a[2]-k^2*a[1]*beta[0]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]-9*mu^2*alpha[1]^2*a[1]*(1/4)-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]-(1/4)*lambda*beta[0]^2*a[1]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-20*mu*lambda*beta[0]*alpha[1]^4*a[4]-7*mu*lambda*beta[0]*a[5]*alpha[1]^2+(2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-4*lambda*beta[0]*alpha[1]^3*a[3]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4]-mu*lambda*alpha[1]^3*a[5]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]-2*k^2*a[1]*alpha[1]*beta[0]-(1/2)*lambda*beta[0]*alpha[1]*a[1]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))-w*beta[0]^2)/G(xi)^2+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+3*beta[0]^2*alpha[1]*a[2]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)+8*mu*beta[0]*alpha[1]^3*a[3]-2*lambda*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]-6*mu^2*alpha[1]^3*a[5]-10*lambda*beta[0]^2*alpha[1]^3*a[4]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+beta[0]^3*a[2]-14*mu^2*beta[0]*a[5]*alpha[1]^2+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+mu*beta[0]^2*a[1]-lambda*beta[0]^3*a[5]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3])/G(xi)^3+((4*beta[0]^3*alpha[1]*a[3]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^3*a[5]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+20*mu*beta[0]^2*alpha[1]^3*a[4]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0])*(diff(G(xi), xi))+20*mu*beta[0]^3*alpha[1]^2*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*beta[0]*alpha[1]^4*a[4]+beta[0]^4*a[3]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+3*mu*beta[0]^3*a[5]+5*beta[0]^4*alpha[0]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4))/G(xi)^4+(((lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5]+5*beta[0]^4*alpha[1]*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4])*(diff(G(xi), xi))+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+beta[0]^5*a[4])/G(xi)^5 = 0

indets(G1)

{k, lambda, mu, w, xi, B[1], B[2], a[1], a[2], a[3], a[4], a[5], alpha[0], alpha[1], beta[0], G(xi), diff(G(xi), xi)}

(2)

``

(3)

eq0 := 5*lambda^2*a[4]*alpha[0]*alpha[1]^4+lambda^2*a[3]*alpha[1]^4-10*lambda*a[4]*alpha[0]^3*alpha[1]^2+k^2*lambda*a[1]*alpha[1]^2-6*lambda*a[3]*alpha[0]^2*alpha[1]^2+a[4]*alpha[0]^5-k^2*a[1]*alpha[0]^2-3*lambda*a[2]*alpha[0]*alpha[1]^2+a[3]*alpha[0]^4+lambda*w*alpha[1]^2+a[2]*alpha[0]^3-w*alpha[0]^2 = 0

``

eq1 := lambda^2*a[4]*alpha[1]^5-10*lambda*a[4]*alpha[0]^2*alpha[1]^3-4*lambda*a[3]*alpha[0]*alpha[1]^3+5*a[4]*alpha[0]^4*alpha[1]-2*k^2*a[1]*alpha[0]*alpha[1]-lambda*a[2]*alpha[1]^3+4*a[3]*alpha[0]^3*alpha[1]+3*a[2]*alpha[0]^2*alpha[1]-2*w*alpha[0]*alpha[1] = 0

eq2 := lambda^2*beta[0]*a[5]*alpha[1]^2+6*mu*alpha[1]^2*alpha[0]*a[2]-2*mu*k^2*a[1]*alpha[1]^2-(1/2)*mu*alpha[1]^2*lambda*a[1]+20*mu*alpha[1]^2*alpha[0]^3*a[4]+12*mu*alpha[1]^2*alpha[0]^2*a[3]-(1/2)*lambda*a[1]*alpha[0]*beta[0]-2*k^2*a[1]*alpha[0]*beta[0]-3*lambda*beta[0]*alpha[1]^2*a[2]-lambda*beta[0]*a[5]*alpha[0]^2+5*lambda^2*beta[0]*alpha[1]^4*a[4]-4*mu*lambda*alpha[1]^4*a[3]-2*mu*w*alpha[1]^2+5*beta[0]*alpha[0]^4*a[4]+4*beta[0]*alpha[0]^3*a[3]+3*beta[0]*alpha[0]^2*a[2]-2*w*alpha[0]*beta[0]-20*mu*lambda*alpha[1]^4*alpha[0]*a[4]-2*mu*alpha[1]^2*lambda*a[5]*alpha[0]-30*lambda*beta[0]*alpha[1]^2*alpha[0]^2*a[4]-12*lambda*beta[0]*alpha[1]^2*alpha[0]*a[3] = 0

NULL

eq3 := (1/4)*(3*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[1]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*k^2*a[1]*alpha[1]^2+(1/2)*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^2*lambda*a[1]+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]^2*a[3]-30*lambda*beta[0]^2*alpha[1]^2*alpha[0]*a[4]-20*mu*beta[0]*lambda*alpha[1]^4*a[4]+(4*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^2*a[5]*alpha[0]-12*mu^2*alpha[1]^2*a[5]*alpha[0]+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*alpha[0]*a[2]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^2*lambda*a[5]*alpha[0]-7*mu*beta[0]*lambda*a[5]*alpha[1]^2+24*mu*beta[0]*alpha[1]^2*alpha[0]*a[3]-9*mu^2*alpha[1]^2*a[1]*(1/4)-w*beta[0]^2+3*beta[0]^2*alpha[0]*a[2]-(1/4)*lambda*beta[0]^2*a[1]-k^2*a[1]*beta[0]^2+10*beta[0]^2*alpha[0]^3*a[4]+6*beta[0]^2*alpha[0]^2*a[3]-(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*w*alpha[1]^2+3*mu*a[1]*alpha[0]*beta[0]*(1/2)+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^4*a[3]+3*mu*beta[0]*a[5]*alpha[0]^2-6*lambda*beta[0]^2*alpha[1]^2*a[3]-2*lambda*beta[0]^2*a[5]*alpha[0]+6*mu*beta[0]*alpha[1]^2*a[2]+60*mu*beta[0]*alpha[1]^2*alpha[0]^2*a[4] = 0

eq4 := 2*mu*alpha[1]^3*a[2]-2*w*alpha[1]*beta[0]-20*lambda*beta[0]*alpha[1]^3*alpha[0]*a[4]-2*lambda*beta[0]*a[5]*alpha[1]*alpha[0]-2*k^2*a[1]*alpha[1]*beta[0]+20*beta[0]*alpha[1]*alpha[0]^3*a[4]+12*beta[0]*alpha[1]*alpha[0]^2*a[3]+6*beta[0]*alpha[1]*alpha[0]*a[2]+8*mu*alpha[1]^3*alpha[0]*a[3]+mu*alpha[1]*a[5]*alpha[0]^2+(1/2)*mu*alpha[1]*alpha[0]*a[1]-4*lambda*beta[0]*alpha[1]^3*a[3]-lambda*alpha[1]^3*mu*a[5]-(1/2)*lambda*beta[0]*alpha[1]*a[1]+20*mu*alpha[1]^3*alpha[0]^2*a[4]-4*mu*lambda*alpha[1]^5*a[4] = 0

eq5 := -6*mu^2*alpha[1]^3*a[5]+(2*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*alpha[1]^3*a[5]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]^3*a[2]+(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2)*alpha[1]^5*a[4]+3*beta[0]^2*alpha[1]*a[2]+40*mu*beta[0]*alpha[1]^3*alpha[0]*a[4]+8*mu*beta[0]*a[5]*alpha[1]*alpha[0]+30*beta[0]^2*alpha[1]*alpha[0]^2*a[4]+12*beta[0]^2*alpha[1]*alpha[0]*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]*a[5]*alpha[0]^2+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*alpha[1]*alpha[0]*a[1]+8*mu*beta[0]*alpha[1]^3*a[3]+3*mu*beta[0]*alpha[1]*a[1]*(1/2)-10*lambda*beta[0]^2*alpha[1]^3*a[4]-2*lambda*beta[0]^2*a[5]*alpha[1]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*alpha[0]^2*a[4]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*lambda*a[5] = 0

eq6 := -14*mu^2*beta[0]*a[5]*alpha[1]^2+beta[0]^3*a[2]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)*a[1]*alpha[0]*beta[0]+12*mu*beta[0]^2*alpha[1]^2*a[3]+6*mu*beta[0]^2*a[5]*alpha[0]-10*lambda*beta[0]^3*alpha[1]^2*a[4]+(6*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*a[5]*alpha[1]^2+(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*a[2]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[0]^2+(5*(-(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*lambda+4*mu^2))*beta[0]*alpha[1]^4*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*a[3]+(2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[1]+10*beta[0]^3*alpha[0]^2*a[4]+4*beta[0]^3*alpha[0]*a[3]-lambda*beta[0]^3*a[5]+mu*beta[0]^2*a[1]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^4*alpha[0]*a[4]+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^2*a[5]*alpha[0]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]^2*a[4]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*lambda*a[5]*alpha[1]^2+(12*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^2*alpha[0]*a[3]+60*mu*beta[0]^2*alpha[1]^2*alpha[0]*a[4] = 0

eq7 := 4*beta[0]^3*alpha[1]*a[3]+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*alpha[0]*a[4]+(8*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*a[5]*alpha[1]*alpha[0]+20*beta[0]^3*alpha[1]*alpha[0]*a[4]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]^3*a[3]+(5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*alpha[1]^3*mu*a[5]+(1/2)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*alpha[1]*a[1]+20*mu*beta[0]^2*alpha[1]^3*a[4]+7*mu*beta[0]^2*a[5]*alpha[1]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*mu*alpha[1]^5*a[4] = 0

eq8 := 4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[5]*alpha[0]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*alpha[0]*a[4]+beta[0]^4*a[3]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*a[3]+(4*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[0]+20*mu*beta[0]^3*alpha[1]^2*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^4*a[3]+3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^2*a[1]*(1/4)+5*beta[0]^4*alpha[0]*a[4]+3*mu*beta[0]^3*a[5]+(1/4)*(3*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[1]+(30*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^2*alpha[0]*a[4]+(17*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*a[5]*alpha[1]^2+(20*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]*mu*alpha[1]^4*a[4] = 0

eq9 := (10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*alpha[1]^3*a[4]+(6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^2*a[5]*alpha[1]+5*beta[0]^4*alpha[1]*a[4]+(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^5*a[4]+2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*alpha[1]^3*a[5] = 0

eq10 := (2*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*a[5]+beta[0]^5*a[4]+5*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*alpha[1]^4*a[4]+6*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda)^2*beta[0]*a[5]*alpha[1]^2+(10*(lambda*B[1]^2-lambda*B[2]^2-mu^2/lambda))*beta[0]^3*alpha[1]^2*a[4] = 0

 

with(LargeExpressions)

COEFFS := solve({eq0, eq1, eq10, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {w, a[1], a[2], alpha[0], alpha[1], beta[0]})

Download by_hand!.mw

Substituting the solutions into the ODE doesn't yield zero, despite the code appearing correct—suggesting either complexity, symbolic limits, or an implementation issue.

 

 

17-ode.mw

 

also in this ode why solution is like this how i can fixed this too

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

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

(1)

ode := diff(G(xi), xi) = sqrt(C*G(xi)^4+B*G(xi)^2+A)

diff(G(xi), xi) = (C*G(xi)^4+B*G(xi)^2+A)^(1/2)

(2)

dsolve(ode, G(xi))

xi-Intat(1/(C*_a^4+B*_a^2+A)^(1/2), _a = G(xi))+c__1 = 0

(3)
 

NULL

Download v1.mw

This question is actually on behalf of a colleague who works with fuzzy mathematics. He typically computes things like fuzzy derivatives by hand, including for specific functions such as "function 14" (though I'm not familiar with the specific form of that function). He’s interested in whether Maple can symbolically and numerically handle tasks in fuzzy calculus — especially taking and plotting fuzzy derivatives.

I’m not experienced with fuzzy systems myself, but I’d like to recommend Maple to him if it supports these features. So my main questions are:

  1. Can Maple compute and plot fuzzy functions and their derivatives?

  2. Does Maple have built-in support or packages for fuzzy arithmetic or fuzzy calculus?

  3. If not natively, is there a workaround or external library that integrates with Maple to do this?

I’d really appreciate any insights or examples. It seems like a missed opportunity for my friend to be doing all this manually when such software might already handle it.

Thanks in advance!

 

I'm trying to collect all terms involving the expression diff(G(xi), xi)/G(xi) in a symbolic equation using . While it's straightforward to do this by hand, I want to automate it in code — ideally by extracting the coefficient of this entire expression directly. However, when I use collect, Maple treats diff(G(xi), xi) and G(xi) separately, and I can't seem to group terms properly by the full ratio diff(G(xi), xi)/G(xi).

Is there a clean way or built-in Maple function to automatically collect or isolate the coefficient of diff(G(xi), xi)/G(xi) as a whole, without having to manually substitute or restructure the expression?

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)

L := (-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(2*a[2]*lambda^2+3*lambda*a[1]+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(2*a[2]*lambda^2+3*lambda*a[1]+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*lambda*a[2]*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*lambda*a[2]*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

(2)

``

(3)

collect(%, {1/(diff(G(xi), xi)), G(xi)})

(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4/G(xi)^4+(f*g^3*(10*lambda*a[2]+2*a[1])-f^3*g*(10*lambda*a[2]+2*a[1])+12*f*g*a[1]*a[2])*(diff(G(xi), xi))^3/G(xi)^3+(f*g^3*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))-4*f*p*a[2]-6*k*l*a[2]-f^3*g*(3*lambda*a[1]+2*a[2]*lambda^2+10*mu*a[2]+2*a[2]*(lambda^2-mu))+6*f*g*(2*a[0]*a[2]+a[1]^2))*(diff(G(xi), xi))^2/G(xi)^2+(f*g^3*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)-4*f*p*a[1]-6*k*l*a[1]-f^3*g*(a[1]*(lambda^2-mu)+3*a[1]*mu+6*a[2]*lambda*mu)+12*f*g*a[0]*a[1])*(diff(G(xi), xi))/G(xi)+f*g^3*(lambda*mu*a[1]+2*mu^2*a[2])-4*f*p*a[0]-6*k*l*a[0]-f^3*g*(lambda*mu*a[1]+2*mu^2*a[2])+6*f*g*a[0]^2 = 0

(4)

L1 := %

num := numer(lhs(L)); num := expand(num); num_collected := collect(num, [1/(diff(G(xi), xi)), G(xi)]); eqs := [seq(coeff(num_collected, {1/(diff(G(xi), xi)), G(xi)}, i) = 0, i = 0 .. 8)]

[(-6*f^3*g*a[2]+6*f*g^3*a[2]+6*f*g*a[2]^2)*(diff(G(xi), xi))^4+(-10*f^3*g*lambda*a[2]+10*f*g^3*lambda*a[2]-2*f^3*g*a[1]+2*f*g^3*a[1]+12*f*g*a[1]*a[2])*G(xi)*(diff(G(xi), xi))^3+(-4*f^3*g*lambda^2*a[2]+4*f*g^3*lambda^2*a[2]-3*f^3*g*lambda*a[1]-8*f^3*g*mu*a[2]+3*f*g^3*lambda*a[1]+8*f*g^3*mu*a[2]+12*f*g*a[0]*a[2]+6*f*g*a[1]^2-4*f*p*a[2]-6*k*l*a[2])*G(xi)^2*(diff(G(xi), xi))^2+(-f^3*g*lambda^2*a[1]-6*f^3*g*lambda*mu*a[2]+f*g^3*lambda^2*a[1]+6*f*g^3*lambda*mu*a[2]-2*f^3*g*mu*a[1]+2*f*g^3*mu*a[1]+12*f*g*a[0]*a[1]-4*f*p*a[1]-6*k*l*a[1])*G(xi)^3*(diff(G(xi), xi))+(-f^3*g*lambda*mu*a[1]-2*f^3*g*mu^2*a[2]+f*g^3*lambda*mu*a[1]+2*f*g^3*mu^2*a[2]+6*f*g*a[0]^2-4*f*p*a[0]-6*k*l*a[0])*G(xi)^4 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0, 0 = 0]

(5)

Download collect-coe.mw

I am facing an issue with two algorithms: one runs correctly, while the other fails to execute. The only difference is that the second algorithm includes one additional term. I would like to understand what causes the failure in the second case.

 a while i used this without problem but i don't know what is issue now.

ode-not-run.mw

Error,(in solve)cannot solve expressions with sum(f[ij]*(H[j]*gamma[j] - PS[j]*alpha[j]),j =1 .. N) for H[j]
can any one what can I do for this error?

What's with some of the older posts missing images?  Were they deleted by maplesoft to save space on mapleprimes servers?  (Storage is pretty cheap these days)

I actually replaced some images a while ago, maybe a few years back.  However I've come across the post again and the image is gone ... strange.  Maybe there's an AI at work here clearing out images. 

In some cases the images are just the output of Maple code plots.  That's ok to remove, I guess, but in others, people have used screenshots which contain code that have been removed where in some cases after they're removed make the entire thread useless.  It's not often but it occurs. 

Anyways, does mapleprimes sometimes clear out images?  Or is it an inadvertent effect when some maintenance is performed?

For compution this is not important, for latex, I find  n>0 little more clear to read than 0<n 

Is there a way to tell Maple not to reverse terms on each side of the > just for latex purposes?

It seems Maple does this only for   > and not for  <

I know the latex output follows what is displayed on the screen in Maple. And that is what happens also for display. Maple rewrites n>0 as   0<n.   

I tried changing display->Typesetting level from extended to maple standard but this had no effect. 

Is there a trick to make Maple not all the > to  <  ?

Again, I wanted to do this just for the latex output because for computation and for screen display in worksheet, it is not an the issue for me, as I only use Latex output.

It seems Maple like to make everything  based on "<" internally and that is why it reverses it?

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

latex(n>0,'output'='string'); #why this is reverse on output?

"0<n"

latex(n>m,'output'='string'); #why this is reverse on output?

"m <n"

latex(n<0,'output'='string'); #but this stays the same

"n <0"

latex(n<m,'output'='string'); #but this stays the same

"n <m"

n>0

0 < n

 

 

Download why_reverses_may_1_2025.mw

I’m trying to verify a solution given in the form from  using Maple's odeTest. Even though the paper claims the solution satisfies the ODE, Maple does not simplify the result to zero. Could someone explain why the test fails or suggest the correct way to verify it in Maple?

restart

with(PDEtools)

with(LinearAlgebra)

with(Physics)

with(SolveTools)

undeclare(prime)

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

(1)

_local(gamma)

Warning, A new binding for the name `gamma` has been created. The global instance of this name is still accessible using the :- prefix, :-`gamma`.  See ?protect for details.

 

declare(u(x, t)); declare(U(xi)); declare(u(x, y, z, t)); declare(Q(xi)); declare(V(xi))

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

 

U(xi)*`will now be displayed as`*U

 

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

 

Q(xi)*`will now be displayed as`*Q

 

V(xi)*`will now be displayed as`*V

(2)

NULL

ode := diff(G(xi), xi) = G(xi)*sqrt(A+B*G(xi)^2)

diff(G(xi), xi) = G(xi)*(A+B*G(xi)^2)^(1/2)

(3)

S1 := G(xi) = -sqrt(A/B)*csch(sqrt(A)*(xi+xi[0]))

G(xi) = -(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))

(4)

res := simplify(odetest(S1, ode))

(A/B)^(1/2)*csch(A^(1/2)*(xi+xi[0]))*(A^(1/2)*coth(A^(1/2)*(xi+xi[0]))+(A*coth(A^(1/2)*(xi+xi[0]))^2)^(1/2))

(5)

S2 := G(xi) = sqrt(-A/B)*sec(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))

(6)

res := simplify(odetest(S2, ode))

(-A/B)^(1/2)*sec((-A)^(1/2)*(xi+xi[0]))*((-A)^(1/2)*tan((-A)^(1/2)*(xi+xi[0]))-(-A*tan((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))

(7)

S3 := G(xi) = sqrt(-A/B)*sech(sqrt(A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

(8)

res := simplify(odetest(S3, ode))

(-A^(1/2)*tanh(A^(1/2)*(xi+xi[0]))-(A*tanh(A^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*sech(A^(1/2)*(xi+xi[0]))

(9)

S4 := G(xi) = sqrt(-A/B)*csc(sqrt(-A)*(xi+xi[0]))

G(xi) = (-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

(10)

res := simplify(odetest(S4, ode))

(-(-A)^(1/2)*cot((-A)^(1/2)*(xi+xi[0]))-(-A*cot((-A)^(1/2)*(xi+xi[0]))^2)^(1/2))*(-A/B)^(1/2)*csc((-A)^(1/2)*(xi+xi[0]))

(11)

S5 := G(xi) = cos(sqrt(-A)*(xi+xi[0]))+sin(sqrt(-A)*(xi+xi[0]))

G(xi) = cos((-A)^(1/2)*(xi+xi[0]))+sin((-A)^(1/2)*(xi+xi[0]))

(12)

res := simplify(odetest(S5, ode))

(cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))*(-A)^(1/2)+(B*sin(2*(-A)^(1/2)*(xi+xi[0]))+A+B)^(1/2)*(-cos((-A)^(1/2)*(xi+xi[0]))-sin((-A)^(1/2)*(xi+xi[0])))

(13)

S6 := G(xi) = 1/(sqrt(B)*(xi+xi[0]))

G(xi) = 1/(B^(1/2)*(xi+xi[0]))

(14)

odetest(S6, subs(A = 0, ode))

-csgn(1/(xi+xi[0]))/(B^(1/2)*(xi+xi[0])^2)-1/(B^(1/2)*(xi+xi[0])^2)

(15)

S7 := G(xi) = 1/(sqrt(-B)*(xi+xi[0]))

G(xi) = 1/((-B)^(1/2)*(xi+xi[0]))

(16)

odetest(S7, subs(A = 0, ode))

-(-1/(xi+xi[0])^2)^(1/2)*xi[0]/((-B)^(1/2)*(xi+xi[0])^2)-(-1/(xi+xi[0])^2)^(1/2)*xi/((-B)^(1/2)*(xi+xi[0])^2)-1/((-B)^(1/2)*(xi+xi[0])^2)

(17)

ode2 := diff(G(xi), xi) = A+B*G(xi)^2

diff(G(xi), xi) = A+B*G(xi)^2

(18)

S8 := G(xi) = sgn(A)*sqrt(A/B)*tan(sqrt(A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(A/B)^(1/2)*tan((A*B)^(1/2)*(xi+xi[0]))

(19)

res := simplify(odetest(S8, ode2))

(sgn(A)*(A*B)^(1/2)*(tan((A*B)^(1/2)*xi[0])^2+1)*(tan((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((tan((A*B)^(1/2)*xi)+tan((A*B)^(1/2)*xi[0]))^2*sgn(A)^2+(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2))/(tan((A*B)^(1/2)*xi[0])*tan((A*B)^(1/2)*xi)-1)^2

(20)

NULL

S9 := G(xi) = -sgn(A)*sqrt(A/B)*cot(sqrt(A*B)*(xi+xi[0]))

G(xi) = -sgn(A)*(A/B)^(1/2)*cot((A*B)^(1/2)*(xi+xi[0]))

(21)

res := simplify(odetest(S9, ode2))

(sgn(A)*(A*B)^(1/2)*(cot((A*B)^(1/2)*xi[0])^2+1)*(cot((A*B)^(1/2)*xi)^2+1)*(A/B)^(1/2)-A*((cot((A*B)^(1/2)*xi[0])*cot((A*B)^(1/2)*xi)-1)^2*sgn(A)^2+(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2))/(cot((A*B)^(1/2)*xi[0])+cot((A*B)^(1/2)*xi))^2

(22)

NULL

S9 := G(xi) = sgn(A)*sqrt(-A/B)*tanh(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*tanh((-A*B)^(1/2)*(xi+xi[0]))

(23)

res := simplify(odetest(S9, ode2))

(A*(sgn(A)^2-1)*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))-sgn(A)^2*A+2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A)/(1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

(24)

NULL

S10 := G(xi) = sgn(A)*sqrt(-A/B)*coth(sqrt(-A*B)*(xi+xi[0]))

G(xi) = sgn(A)*(-A/B)^(1/2)*coth((-A*B)^(1/2)*(xi+xi[0]))

(25)

odetest(S10, ode2)

(sgn(A)^2*A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+sgn(A)^2*A-2*sgn(A)*(-A/B)^(1/2)*(-A*B)^(1/2)-A*cosh(2*(-A*B)^(1/2)*(xi+xi[0]))+A)/(-1+cosh(2*(-A*B)^(1/2)*(xi+xi[0])))

(26)

NULL

S11 := G(xi) = -1/(B*(xi+xi[0]))

G(xi) = -1/(B*(xi+xi[0]))

(27)

odetest(S11, subs(A = 0, ode2))

0

(28)

S12 := G(xi) = A*(xi+xi[0])

G(xi) = A*(xi+xi[0])

(29)

odetest(S12, subs(B = 0, ode2))

0

(30)

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Why doesn't this ODE return zero when using odetest? Did I do something wrong?

Would you like help checking the equation or debugging the issue?

restart

with(PDEtools)

declare(P(mu))

P(mu)*`will now be displayed as`*P

(1)

assume(A::real, r::real, rho::real, lambda::real)

Psol := P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*exp(lambda*rho*mu)+r*exp(-lambda*rho*mu))

(2)

ode := (diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

(diff(P(mu), mu))^2-rho^2*P(mu)^2*(1+r*P(mu)^2) = 0

(3)

res := odetest(Psol, ode)

4*A^6*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+8*r*A^4*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-24*A^4*lambda^4*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^6*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^4*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4+4*A^2*r^2*rho^2*lambda^4*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*r*A^4*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^4*lambda^2*rho^2*exp(4*lambda*rho*mu)*r/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(6*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-8*A^2*lambda^2*rho^2*exp(4*lambda*rho*mu)*r^2/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4-4*A^2*r^2*rho^2*lambda^2*exp(2*lambda*rho*mu)/(A^2*exp(2*lambda*rho*mu)+exp(2*lambda*rho*mu)*r+r)^4

(4)

simplify(res)

4*lambda^2*exp(2*lambda*rho*mu)*(((-2*lambda^2-2)*r^2+(-6*lambda^2-2)*A^2*r)*exp(2*lambda*rho*mu)+(lambda+1)*((A^2+r)^2*exp(4*lambda*rho*mu)+r^2)*(lambda-1))*A^2*rho^2/((A^2+r)*exp(2*lambda*rho*mu)+r)^4

(5)

P_hyper := P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

P(mu) = 2*A*lambda/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))

(6)

res_hyper := simplify(odetest(P_hyper, ode), symbolic)

-16*A^4*lambda^2*rho^2*r*(lambda^2+1)/((A^2+r)*cosh(rho*mu)+(A^2-r)*sinh(rho*mu))^4

(7)
 

NULL

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