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Should not dsolve give implicit solution if unable...

Asked by: nm 11363
ode dsolve implicit
15 hours ago
0  2

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?

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

ode:=y(x)*diff(y(x),x) = a;
ic:=y(0) = b;
sol:=dsolve([ode,ic]);

y(x)*(diff(y(x), x)) = a

y(0) = b

> 

sol:=dsolve([ode,ic],'implicit')

-2*a*x+y(x)^2-b^2 = 0

 

 

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?

How find leading order & resonance point ?...

Asked by: salim-barzani 1575
parameters pde differential-equations
Yesterday at 4:39 PM
0  10

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

bug report: int() gives Error, (in tools/eval_foo...

Asked by: nm 11363
integration int indefinite-integration
August 20 2025
1  1

Attached worksheet

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

> 

restart;
> 

integrand:=1/2/x^(9/2)*2^(1/2)*Pi^(1/2)/(1/x)^(1/2)*cos(1/x);

(1/2)*2^(1/2)*Pi^(1/2)*cos(1/x)/(x^(9/2)*(1/x)^(1/2))

> 

int(integrand,x)

Error, (in tools/eval_foo/do) too many levels of recursion

 

 

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).

> 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

> 

restart;
> 

integrand:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

> 

int(integrand,x)

Error, (in type/trig) too many levels of recursion

> 

int(integrand,x)

(1/6)*(-c*(-1+sin(f*x+e)))^(1/2)*((3/4)*B*sin(f*x+e)*tan(f*x+e)*cos(2*f*x+2*e)+A*sin(2*f*x+2*e)-(3/8)*tan(f*x+e)*(((4/5)*B*sin(f*x+e)+A)*sin(3*f*x+3*e)+(44/15)*B*sin(f*x+e)^2+(5*A-6*B)*sin(f*x+e)-(32/3)*A))*a*c^2*(a*(1+sin(f*x+e)))^(1/2)/f

> 

restart;
> 

integrand:=(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2);
int(integrand,x)

(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)

Error, (in type/trig) too many levels of recursion

 

 

Download another_int_error_too_many_levels_maple_2025_1.mw

Splitting a matrix defined on regular and irregula...

Asked by: Muhammad Usman 240
August 19 2025
0  1

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

Does OpenMaple work in the Free Trial?...

Asked by: benshaw2 5
openmaple ubuntu
August 18 2025
1  0

I installed a free trial of Maple 2025, but I can't seem to get the (simple) sample test.java script to run using OpenMaple. It compiles fine, but when I try to run it I get a Segmentation Fault error. I've ensured that the environmental variables, as described in the installation documentation, are given properly. The documentation/example in the installation refers to an old version of Maple, so I wondered if perhaps the free trial version does not have all of the updated components? I was hoping to test my project compatibility with OpenMaple before purchasing Maple.

My OS is Ubuntu 24.04, and I'm using Java 21. It would be nice to get everything running in IntelliJ eventually, but for now even trying to run in the terminal is problematic.

How make simplify the fractional expresion?...

Asked by: salim-barzani 1575
radical simplify simplification
August 15 2025
2  1

In thus manuscript i got some reviewer comment which is asked to simplify this expresion and there is a lot of them maybe if i do by hand i  made a mistake becuase a lot of variable so how i can fix this issue and make thus square root are very simple as they demand

> 

restart
> 

B[2] := 0

0

 (1)

K := sqrt(-(1/2)*sqrt(2)*sqrt(lambda*a[5]/a[4])+sqrt(-a[5]/(2*a[4]))*(B[1]*sqrt(-lambda)*sinh(xi*sqrt(-lambda))+B[2]*sqrt(-lambda)*cosh(xi*sqrt(-lambda)))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda)+sqrt(-(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(2*lambda*a[4]))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda))*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

 (2)
> 

simplify(K)

(1/2)*exp(I*((k*v+w)*tau^alpha+alpha*(k*xi+gamma))/alpha)*2^(3/4)*((lambda*(a[5]*(-lambda^2*B[1]^2+mu^2)/(lambda*a[4]))^(1/2)+(-B[1]*cosh(xi*(-lambda)^(1/2))*lambda-mu)*(lambda*a[5]/a[4])^(1/2)+sinh(xi*(-lambda)^(1/2))*lambda*(-a[5]/a[4])^(1/2)*(-lambda)^(1/2)*B[1])/(B[1]*cosh(xi*(-lambda)^(1/2))*lambda+mu))^(1/2)

 (3)

subsindets(K, `&*`(rational, anything^(1/2)), proc (u) options operator, arrow; (u^2)^(1/2) end proc)

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

 (4)

latex(%)

\frac{\sqrt{-2 \sqrt{2}\, \sqrt{\frac{\lambda  a_{5}}{a_{4}}}+\frac{2 \sqrt{-\frac{2 a_{5}}{a_{4}}}\, B_{1} \sqrt{-\lambda}\, \sinh \left(\xi  \sqrt{-\lambda}\right)}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}+\frac{2 \sqrt{-\frac{2 \left(\lambda^{2} B_{1}^{2} a_{5}-\mu^{2} a_{5}\right)}{\lambda  a_{4}}}}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}}\, {\mathrm e}^{\mathrm{I} \left(k \left(\xi +\frac{v \,\tau^{\alpha}}{\alpha}\right)+\frac{w \,\tau^{\alpha}}{\alpha}+\gamma \right)}}{2}

  

KK := sqrt(-(1/2)*sqrt(2)*sqrt(lambda*a[5]/a[4])+sqrt(-a[5]/(2*a[4]))*(B[1]*sqrt(-lambda)*sinh(xi*sqrt(-lambda))+B[2]*sqrt(-lambda)*cosh(xi*sqrt(-lambda)))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda)+sqrt(-(lambda^2*B[1]^2*a[5]-lambda^2*B[2]^2*a[5]-mu^2*a[5])/(2*lambda*a[4]))/(B[1]*cosh(xi*sqrt(-lambda))+B[2]*sinh(xi*sqrt(-lambda))+mu/lambda))*exp(I*(k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma))

(1/2)*(-2*2^(1/2)*(lambda*a[5]/a[4])^(1/2)+2*(-2*a[5]/a[4])^(1/2)*B[1]*(-lambda)^(1/2)*sinh(xi*(-lambda)^(1/2))/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda)+2*(-2*(lambda^2*B[1]^2*a[5]-mu^2*a[5])/(lambda*a[4]))^(1/2)/(B[1]*cosh(xi*(-lambda)^(1/2))+mu/lambda))^(1/2)*exp((k*(xi+v*tau^alpha/alpha)+w*tau^alpha/alpha+gamma)*I)

 (5)

latex(KK)

\frac{\sqrt{-2 \sqrt{2}\, \sqrt{\frac{\lambda  a_{5}}{a_{4}}}+\frac{2 \sqrt{-\frac{2 a_{5}}{a_{4}}}\, B_{1} \sqrt{-\lambda}\, \sinh \left(\xi  \sqrt{-\lambda}\right)}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}+\frac{2 \sqrt{-\frac{2 \left(\lambda^{2} B_{1}^{2} a_{5}-\mu^{2} a_{5}\right)}{\lambda  a_{4}}}}{B_{1} \cosh \left(\xi  \sqrt{-\lambda}\right)+\frac{\mu}{\lambda}}}\, {\mathrm e}^{\mathrm{I} \left(k \left(\xi +\frac{v \,\tau^{\alpha}}{\alpha}\right)+\frac{w \,\tau^{\alpha}}{\alpha}+\gamma \right)}}{2}

  

NULL

Download simplify.mw

How can I=sqrt(-1) can be properly factored out fr...

Asked by: Ahmed111 140
radical simplify simplification
August 15 2025
1  3

I am trying to factor out I = sqrt(-1) from square roots in my Maple expression by using a substitution f2. However, after applying these substitutions to my final expression, there is no visible change. In addition, the term sqrt(2)/2 + sqrt(2)*I/2 also appear. How can I=sqrt(-1) can be properly factored out from the square roots?

> 

restart
> 

with(Student[Precalculus])
> 

interface(showassumed = 0)
> 

assume(x::real); assume(t::real); assume(lambda1::complex); assume(lambda2::complex); assume(a::real); assume(A__c::real); assume(B1::real); assume(B2::real); assume(delta1::real); assume(delta2::real); assume(`ω__0`::real); assume(g::real); assume(l__0::real)
> 

expr := (0*A__c)*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)+(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t)))*(sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)*(((-sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))-sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))+exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))))*exp(-2*sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(l__0^2*(I*delta1-delta2)*t*`ω__0`+(1/2)*x))+exp(sqrt(-A__c^2*g+(delta1+I*delta2)^2)*(x+(2*I)*`ω__0`*l__0^2*(delta1+I*delta2)*t))*((sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))*sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2)))*exp((2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))-exp(-(2*(l__0^2*(I*delta1+delta2)*t*`ω__0`-(1/2)*x))*sqrt(-A__c^2*g+(delta1-I*delta2)^2))*(sqrt(delta1+I*delta2-sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2+sqrt(-A__c^2*g+(delta1-I*delta2)^2))+sqrt(delta1+I*delta2+sqrt(-A__c^2*g+(delta1+I*delta2)^2))*sqrt(-delta1+I*delta2-sqrt(-A__c^2*g+(delta1-I*delta2)^2)))))*(-delta1+I*delta2)*(delta1+I*delta2))

(2*I)*exp(-I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t)))*((-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2)))*delta2/(exp(I*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(((-(delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)-(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))+exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)))*exp(-2*(-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(l__0^2*(I*delta1-delta2)*t*omega__0+(1/2)*x))+exp((-A__c^2*g+(delta1+I*delta2)^2)^(1/2)*(x+(2*I)*omega__0*l__0^2*(delta1+I*delta2)*t))*(((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)*(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2))*exp(2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))-exp(-2*(l__0^2*(I*delta1+delta2)*t*omega__0-(1/2)*x)*(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))*((delta1+I*delta2-(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2+(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2)+(delta1+I*delta2+(-A__c^2*g+(delta1+I*delta2)^2)^(1/2))^(1/2)*(-delta1+I*delta2-(-A__c^2*g+(delta1-I*delta2)^2)^(1/2))^(1/2))))*(I*delta2-delta1)*(delta1+I*delta2))

 (1)
> 

`assuming`([simplify(combine(simplify(convert(combine(eval(expr, delta1 = 0)), trigh))))], [delta2 > g*A__c and g*A__c > 0])

(cos((2*A__c^2*g*l__0^2-1)*omega__0*t)-I*sin((2*A__c^2*g*l__0^2-1)*omega__0*t))*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*delta2+(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*(-A__c^2*g-delta2^2)^(1/2))/(delta2*(I*(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))+delta2))

 (2)
> 

f1 := simplify(convert(numer(%),exp))/factor(denom(%))

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*delta2+(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*(-A__c^2*g-delta2^2)^(1/2))*(-A__c^2*g-delta2^2)^(1/2))/((-(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*(-A__c^2*g-delta2^2)^(1/2))+I*delta2)*delta2)

 (3)
> 

sqrtterms := indets(%, sqrt)

{(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2), (I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2), (-A__c^2*g-delta2^2)^(1/2)}

 (4)
> 

f2 := subs({sqrtterms[1] = sqrt(I)*sqrt(delta2-sqrt(-A__c^2*g-delta2^2)/(I)), sqrtterms[2] = sqrt(I)*sqrt(delta2+sqrt(-A__c^2*g-delta2^2)/(I)), sqrtterms[3] = sqrt(I)*sqrt(A__c^2*g+delta2^2)})

{(I*delta2-(-A__c^2*g-delta2^2)^(1/2))^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2), (I*delta2+(-A__c^2*g-delta2^2)^(1/2))^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2), (-A__c^2*g-delta2^2)^(1/2) = ((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2)}

 (5)
> 

f3 := subs(f2, f1)

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*(A__c^2*g+delta2^2)^(1/2))+I*delta2)*delta2)

 (6)
> 

f4 := subs({sqrt(A__c^2*g+delta2^2) = Z}, f3)

I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)+I*delta2)*delta2)

 (7)
> 

f4f := A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*`ω__0`*t)+f4

A__c*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)+I*exp(-(2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(-I*cosh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0-(1/2)*x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))^2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0-x)*((1/2)*2^(1/2)+((1/2)*I)*2^(1/2))*Z)+I*delta2)*delta2)

 (8)
> 

f4fnl := subs({I = -I, x = -x}, f4f)

A__c*exp((2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)-I*exp((2*I)*(A__c^2*g*l__0^2-1/2)*omega__0*t)*(I*cosh(4*(l__0^2*delta2*t*omega__0+(1/2)*x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)*delta2+((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))^2*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)+sinh(4*(l__0^2*delta2*t*omega__0+(1/2)*x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)/((-((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))^2*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh(2*(2*delta2*l__0^2*t*omega__0+x)*((1/2)*2^(1/2)-((1/2)*I)*2^(1/2))*Z)-I*delta2)*delta2)

 (9)
> 

Mdensity := simplify(f4f*f4fnl)

(1/4)*(2*(1-I*A__c*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)*delta2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)-2*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)*delta2+(1+I)*2^(1/2)*Z*sinh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)+(2*I)*A__c*delta2^2)*(2*(I*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*A__c-1)*delta2*cosh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)+(1-I)*2^(1/2)*Z*sinh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)-(2*I)*A__c*delta2^2+2*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2))/(delta2^2*((delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh((1+I)*(2*delta2*l__0^2*t*omega__0-x)*2^(1/2)*Z)-delta2)*((delta2-I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*(delta2+I*(-A__c^2*g-delta2^2)^(1/2))^(1/2)*cosh((1-I)*(2*delta2*l__0^2*t*omega__0+x)*2^(1/2)*Z)-delta2))

 (10)

NULL

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how to navigate to output label...

Asked by: Frank Garvan 5
worksheet equation-label
August 11 2025
1  0

Is there a short-cut for jumping to a specific output label in a Maple worksheet?

I have a Maple worksheet with over 200 labels:  (1), (2), ....., (236) etc?

"Find" does not seem to work.

Thanks

Frank Garvan

Unable to connect to Matlab using openlink()...

Asked by: Youthdoo 10
August 08 2025
2  0

I have Maple 2016 and Matlab 2016b installed on my Windows destop.

When I run

with(Matlab);
openlink()

in a Maple worksheet the following error window appears.

After closing the window I also see the following error message,

Error, (in Matlab:-openlink) there was a problem finding or loading matlink.dll. Refer to ?Matlab,setup for help configuring your system to work with the Matlab-link.

How to fix the connection from Maple to Matlab?

How to prove this result?...

Asked by: sand15 872
statistics integration pdf
August 05 2025
0  0


A classical probability result says that if G1 and G2 are two independent Gamma random variables with same scale parameter (let's say 1 to simplify) and shape parameters a1 and a2 respectively, then Gk / (G1 + G2 ) is a Beta random variable with parameters (ak , a3-k ) (k=1..2).

In the attached file it is shown that (Maple 2015) function Statistics:-PDF fails in computing the PDF of Gk.
Noting strange here if you observe that even in the extremely simple case Z = X / (X+Y), where both X and Y are independent Uniform random variable with support [0, 1), Maple 2015 already fails in computing PDF(Z).

An alternative to Statistics:-PDF is to write explicitely the double integration which defines CDF(Z) (to begin with, and later PDF(Gk)) and ask Maple to do the integrations.
This approach works for Z but requires helping Maple when X and Y are still independent Uniform random variables but with respective non instanciated supports [0, a1) and [0, a2).

Applying to the Gamma-Gamma case the recipies I introduced in the Uniform-Uniform case does not give any result, unless in the very particular case where the shape parameters a1 and a2 are (strictly) positive integers.

All the details are in X_over_(X_plus_Y).mw

Do you have any idea how to prove with Maple the probability result mentioned at the head of this question?

PS: The "classical method" to do compute PDF(Z) consists in changing the integration variables < x1, x2 > into < x1 = v1v2, x2 = v2 (1-v1) > (see for instance Stack exchange)... but even after having dome it I still cannot get the desired result.

Thanks in advance.

Maple freezes with copy-paste...

Asked by: Bachatero 45
gui crash editing
July 30 2025
0  1

I experience the following quirk using maple 2025 in worksheet mode: copy a formula and then paste it can often freeze the program. Termination only via ctrl-Alt-delete task manager. Has anybody similar problems or should i think that is happening only in my case?

Strange behavior for noncommutative (dot) multipli...

Asked by: vv 13847
July 26 2025
3  5 
f(a).b;            #ok
                           (f(a)) . b

op(0, f(a).b);     #ok
                               .

lprint(f(a).b);    #ok
f(a) . b

f(7).b;            #???
                             f(7) b

op(0, f(7).b);     #???
                               *

lprint(f(7).b);    #???
f(7)*b

 

How can I plot a bifurcation diagram?...

Asked by: GFY 65
ode differential-equations bifurcation
July 23 2025
0  3

I'm working on a system of coupled ordinary differential equations with multiple degrees of freedom. I would like to explore the existence of multiple solutions by using a bifurcation diagram. To this end, I tried using the built-in Bifurcation command in Maple. However, the command repeatedly returns errors and fails to produce the expected plots.

Has anyone successfully used the Bifurcation command in Maple for coupled ODE systems? Are there specific settings or prerequisites that I might be missing? I would greatly appreciate any guidance or example code demonstrating how to properly use this command for such systems.
bifurcation.mw

Why is Maple 2025.1 not listed in Windows 11 Snap ...

Asked by: C_R 3437
windows11
July 23 2025
2  0

To organize windows, Windows 11 provides a new function "Snap Layout". The example screen shot below shows options to place the Maple 2025 Screen Reader window.  

Ein Bild, das Screenshot, Reihe, Software, Multimedia-Software enthält. KI-generierte Inhalte können fehlerhaft sein.

Draging now Maple 2025.1 Screen Reader to the left window of the third option results in the following selection screen

Ein Bild, das Text, Screenshot, Software, Computersymbol enthält. KI-generierte Inhalte können fehlerhaft sein.

where on the right a list of tasks to chose from is presented. In this list Maple 2025.1 is missing. However Maple 2025.1 was running as can be seen from the task bar.

Has anybody managed to position Maple 2025.1 windows with the Snap Layout (or alternatively with Win+Arrow keys) or at least reproduce what I see on my computer?

Why can a Maple 2025.1 window be adjusted by hand but Windows does not do this in Snap Layout?

(Dragging and adjusting a Maple window by hand is not an option. This is how we had to work before Windows 7.)

How remove this sign Root0f- even use allvalues i...

Asked by: Math-dashti 95
solve implicit allvalues
June 27 2025
1  2

what is problem in here

> 

restart;
> 

with(plots):
> 

with(LinearAlgebra):
> 

with(DEtools):

diff(u(x), x) = f(u(x), v(x)), diff(v(x), x) = g(u(x), v(x)) for the two differential equations.

> 

f := (u,v) -> u+cos(v);
g := (u,v) -> u*v-v+sin(v);

proc (u, v) options operator, arrow; u+cos(v) end proc

  

proc (u, v) options operator, arrow; v*u-v+sin(v) end proc

 (1)

The equilibria:

> 

equilibria := solve({f(u,v)=0, g(u,v)=0}, {u,v},explicit);

{u = 1, v = Pi}, {u = -cos(RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z)), v = RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z)}

 (2)
> 

allvalues(RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z))

RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, 1.306542374), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, -1.306542374), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, -2.331122370), RootOf(sin(_Z)*_Z^2+sin(_Z)-2*_Z, 2.331122370), 0

 (3)
 

NULL

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