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Riccati equation...

Asked by: Zeineb 540
ode dsolve differential-equations
Yesterday at 6:52 PM
0  3

Dear all

I get error when solving Riccati equation. I want to get six different solution. 

ricatti_equation.mw

thank you for your help

why pdsolve fail when adding Physics:-Setup(assumi...

Asked by: nm 11218
assuming pde pdsolve
May 18 2025
2  0

Same exact code. When adding Physics:-Setup(assumingusesAssume = true):  before, now pdsolve do not give solution.

Removing Physics:-Setup(assumingusesAssume = true): now it works.

Why? Should not solution be returned in both cases?

> 

interface(version);

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

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1872 and is the same as the version installed in this computer, created 2025, May 17, 22:58 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

> 

restart;

Example 1. Adding Physics:-Setup(assumingusesAssume = true): makes pdsolve fail

 
> 

Physics:-Setup(assumingusesAssume = true):

> 

pde := diff(u(r, t), t) = k*diff(u(r, t), r$2):
ic  := u(r,0)=r*f(r):
bc  := u(0,t)=0,u(a,t)=a*phi(t):
sol:= pdsolve({pde, ic, bc}, u(r, t));

> 

 

> 

 

Example 2. Same code but removing Physics:-Setup(assumingusesAssume = true): makes it work

 
> 

restart;

> 

pde := diff(u(r, t), t) = k*diff(u(r, t), r$2):
ic  := u(r,0)=r*f(r):
bc  := u(0,t)=0,u(a,t)=a*phi(t):
sol:= pdsolve({pde, ic, bc}, u(r, t));

u(r, t) = Sum(2*sin(n*Pi*r/a)*exp(-k*Pi^2*n^2*t/a^2)*(Int(r*(-phi(0)+f(r))*sin(n*Pi*r/a), r = 0 .. a))/a, n = 1 .. infinity)+Int(Sum(2*sin(n*Pi*r/a)*exp(-k*Pi^2*n^2*(t-tau)/a^2)*(diff(phi(tau), tau))*a*(-1)^n/(n*Pi), n = 1 .. infinity), tau = 0 .. t)+r*phi(t)

> 

 


 

Download pdsolve_fail_when_adding_assuming.mw

There is any way for knowing which parameter are r...

Asked by: salim-barzani 1410
solve ode parameters
May 18 2025
1  0

I'm currently working on applying a specific method to solve a nonlinear equation. However, I've encountered a recurring issue: during the process, I often cannot determine certain parameters, which forces me to abandon the solution or switch to a different method. This has happened multiple times and is disrupting my goal of applying all intended methods consistently to a single equation.

In particular, I’m struggling to identify the correct parameters for U(ξ), which are essential for the solution. This challenge is not limited to one method I’ve faced similar problems in previous attempts, and I’m unsure why these parameters cannot be derived in some cases.

My question is: How can I manage this issue effectively? Is there a reliable way to predict or determine whether the necessary parameters will emerge correctly before fully applying a method?

I would greatly appreciate any insights or strategies you could share to help me handle this problem more systematically.

Thank you in advance for your support.

runing.mw

A simple expression crashes Maple...

Asked by: vv 13650
interrupt simplify crash
May 17 2025
1  4

This simple expression (from a recent post) crashes Maple:

simplify(tan(Pi/5) + sin(Pi/15) - sqrt(15));

In Maple 2025, in a new worksheet, this command crashes Maple; it is not possible to interrupt the computation (with the "Stop" button) and the worksheet must be closed.
In Maple 2024, the computation can be interrupted, but after repeating (maybe twice) the command, the interruption becomes impossible.

Question: is there a simpler command which crashes Maple?

Tiny menu fonts...

Asked by: C_R 3327
font gui windows10
May 16 2025
2  0

Some menu fonts have become smaller under Windows 10 for some reason.
There where no changes of the system settings nor system updates. A system restart did not restore to normal font size. This also on Maple 2024 and lower.

Any ideas what could have caused this and how to restore to normal?

That's from annother Windows 10 system.

 

Pde Question How to impliment the this equations i...

Asked by: KIRAN SAJJAN 40
homework pde pdsolve
May 16 2025
0  12

How to solve these pde equations in maple to get the similar type graphs.

Ode equations we can solve directly but these equations are pde .

in the article they have solved the governing equations by series solution? 

can we solve these equations in maple also by series solution or any other method is there to solve these equations

How can I export high-resolution 3D graphics in Ma...

Asked by: GFY 65
plot3d
May 15 2025
0  7

I have used plot3d in Maple to generate a 3D plot, but I’m not sure how to export it in high resolution. I tried right-clicking to export the image directly, but the SVG output appeared garbled, and the JPEG version was too low in quality. I also attempted to export the plot using commands, but the resulting image still lacked sufficient resolution. I would like to ask how I can properly export a high-quality 3D figure from Maple.

Commands I have tried：

plotsetup(jpeg, plotoutput = "C:/Users/gfy/Desktop/data5151.jpg", plotoptions = `dpi=1200`);
print(ddd);
plotsetup(default);

Page print formating problem Maple 2024...

Asked by: Ronan 1336
pdf export table
May 15 2025
0  3

I have a print format problem in Maple 2024.  For documents I print out, I use a special layout where all the contents are inside a table. The table is rigged to print on A4 paper. This is useful for my math notes. I havent done this for 18+ months. There appears to be a bug in Maple 2024. Only the first page is printed. Things work ok in Maple 2023. Maybe it is a setting difference or corruption in my install. Could somebody confirm this. Also if you can reproduce the problem could you let me know if it is in Maple 2025. I haven't upgraded yet.

 

2025-05-15_Q_page_print_formating.mw 
2025-05-15_Q_page_print_formating_M_2023.pdf
2025-05-15_Q_page_print_formating_M_2024.pdf

Spam recently on mapleprimes...

Asked by: Christopher2222 5975
spam
May 15 2025
2  1

The last few mornings there's been a high rate of spam.  I just deleted 5 or 6 posts.  How are they getting through and why haven't they stopped?

why random internal error Error, (in evala/Factors...

Asked by: nm 11218
allvalues
May 11 2025
3  0

in Maple 2025 on Linux, I see random Error, (in evala/Factors) the modular inverse does not exist from call to allvalues().

Sometimes it happens and sometimes not. Any explanation of this?

 

It seems Maple uses random number generatror to decide when to generate an internal error as I am not able to see a pattern.

> 

interface(version);

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

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1868. The version installed in this computer is 1866 created 2025, May 6, 10:52 hours Pacific Time, found in the directory /home/me/maple/toolbox/2025/Physics Updates/lib/`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

> 

restart;
> 

kernelopts('assertlevel'=2):
> 

sol:=[1/3*exp(RootOf(-5*I*Pi-ln(256/(x+1)^6/(exp(_Z)^81+9)*(exp(_Z)^81+3)^3)+162*_Z))^81+2];
allvalues(sol);

[(1/3)*(exp(RootOf(-(5*I)*Pi-ln(256*((exp(_Z))^81+3)^3/((x+1)^6*((exp(_Z))^81+9)))+162*_Z)))^81+2]

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

 


 

Download why_fail_sometimes_may_11_2025_V2.mw

Update was able to produce this also in Maple 2024.2 on windows

> 

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 1868. The version installed in this computer is 1849 created 2025, March 12, 12:37 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

> 

restart;
> 

kernelopts('assertlevel'=2):
sol:=[1/3*exp(RootOf(-5*I*Pi-ln(256/(x+1)^6/(exp(_Z)^81+9)*(exp(_Z)^81+3)^3)+162*_Z))^81+2];
allvalues(sol);

[(1/3)*(exp(RootOf(-(5*I)*Pi-ln(256*((exp(_Z))^81+3)^3/((x+1)^6*((exp(_Z))^81+9)))+162*_Z)))^81+2]

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

`[Length of output exceeds limit of 100000]`

> 

allvalues(sol);

Error, (in evala/Factors) the modular inverse does not exist

> 

 


 

Download modular_inverse_maple_2024_2.mw

 

Error, (in content/gcd) too many levels of recursi...

Asked by: nm 11218
ode differential-equations odetest
May 07 2025
0  0

I do not remember seeing this before or reporting. Just in case, here is how to reproduce it. This happens also in Maple 2024.2

The problem with these errors is that they can not be cought using try/catch.

I was testing a solution which most likely wrong, but I get 

                 Error, (in content/gcd) too many levels of recursion

> 

interface(version);

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

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1866 and is the same as the version installed in this computer, created 2025, May 6, 10:52 hours Pacific Time.`

> 

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 17 and is the same as the version installed in this computer, created May 5, 2025, 12:37 hours Eastern Time.`

> 

restart;
> 

sol:=ln((1/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)+1)^(1/3)/(1/81*u(x)^2*6^(2/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)^2-1/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)+1)^(1/6))+1/3*3^(1/2)*arctan(1/3*(2/9*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)-1)*3^(1/2)) = Int(3/2*(-32*x^(15/2)-6480*A^2*x^(9/2)-65610*A^4*x^(3/2)+720*A*x^6+29160*A^3*x^3+59049*A^5)/surd(-A*(-2*x^(3/2)+9*A)/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4),3)/(-128*x^11-54432*A^2*x^8-1837080*A^4*x^5+4782969*A^7*x^(1/2)-7440174*A^6*x^2+4960116*A^5*x^(7/2)+408240*A^3*x^(13/2)+4032*A*x^(19/2))*A*6^(1/3),x)+2*_C1;
ode:=diff(u(x),x) = -1/18/x^(1/2)*(-576*A*x^(9/2)-11664*A^3*x^(3/2)+32*x^6+3888*A^2*x^3+13122*A^4)/(-2*x^(3/2)+9*A)^3*u(x)^3-1/18/x^(1/2)*(1944*A*x^(5/2)-216*x^4-4374*A^2*x)/(-2*x^(3/2)+9*A)^3*u(x)-1/18/x^(1/2)*(486*A*x^(3/2)-2187*A^2)/(-2*x^(3/2)+9*A)^3;

ln(((1/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)+1)^(1/3)/((1/81)*u(x)^2*6^(2/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)^2-(1/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)+1)^(1/6))+(1/3)*3^(1/2)*arctan((1/3)*((2/9)*u(x)*6^(1/3)/surd((-9*A^2+2*A*x^(3/2))/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)-1)*3^(1/2)) = Int((3/2)*(-32*x^(15/2)-6480*A^2*x^(9/2)-65610*A^4*x^(3/2)+720*A*x^6+29160*A^3*x^3+59049*A^5)*A*6^(1/3)/(surd(-A*(-2*x^(3/2)+9*A)/(-288*A*x^(9/2)-5832*A^3*x^(3/2)+16*x^6+1944*A^2*x^3+6561*A^4), 3)*(-128*x^11-54432*A^2*x^8-1837080*A^4*x^5+4782969*A^7*x^(1/2)-7440174*A^6*x^2+4960116*A^5*x^(7/2)+408240*A^3*x^(13/2)+4032*A*x^(19/2))), x)+2*_C1

diff(u(x), x) = -(1/18)*(-576*A*x^(9/2)-11664*A^3*x^(3/2)+32*x^6+3888*A^2*x^3+13122*A^4)*u(x)^3/(x^(1/2)*(-2*x^(3/2)+9*A)^3)-(1/18)*(1944*A*x^(5/2)-216*x^4-4374*A^2*x)*u(x)/(x^(1/2)*(-2*x^(3/2)+9*A)^3)-(1/18)*(486*A*x^(3/2)-2187*A^2)/(x^(1/2)*(-2*x^(3/2)+9*A)^3)

> 

try
    odetest(sol,ode);
catch:
    print("cought error ok");
end try;

Error, (in content/gcd) too many levels of recursion

 

 

Download content_gce_odetest_error_may_7_2025.mw

How to find what changed in SupportTools after eac...

Asked by: nm 11218
update supporttools
May 06 2025
4  1

I asked similar question 5 years ago about Physics update but it was not possible to find this information

How-To-Find-What-Changed-In-Physics

I'd like to ask now again same about  SupportTools. Can one find out what update is actually included in new version?

Even if it is just 2-3 lines. It will be good if users had an idea what was fixed or improved in the new version.

Any update to software should inlcude such information. Not asking for details, just general information will be nice. Right now one does an update and have no idea at all what the new update fixed or improved which is not good.

May be such information can be displayed on screen after a user updates?

Can we plot this gain function in 3D from pde?...

Asked by: janhardo 630
pde differential-equations plotting
May 05 2025
3  3

Yes , i can ..a procedure for thiis?

> 

restart; with(plots); printf("Step 1: Declare l and b as free variables for the 3D plot.\n"); l := 'l'; b := 'b'; printf("Step 2: Set fixed values for remaining parameters.\n"); a := 1; c := 1; d := .2; f := 1; epsilon := 1; printf("Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.\n"); G := proc (l, b) options operator, arrow; 2*Im(sqrt(-a^2*f*d-a*b+(1/2)*l^2-3*a+(1/2)*sqrt(-48*a^3*f*d+4*epsilon*l^3*c-24*a*epsilon*l*c+l^4+4*l^2*c^2-48*a^2*b-12*a*l^2+36*a^2))) end proc; printf("Step 4: Create a 3D surface plot of G(l,b).\n"); gainPlot := plot3d(G(l, b), l = -6 .. 4, b = .1 .. 1.2, labels = ["Wave number l", "Parameter b", "Gain G(l,b)"], title = "3D MI Gain Spectrum over (l, b)", shading = zhue, axes = boxed, grid = [60, 60]); printf("Step 5: Display the 3D surface plot.\n"); gainPlot

Step 1: Declare l and b as free variables for the 3D plot.
Step 2: Set fixed values for remaining parameters.
Step 3: Define the 3D gain function G(l,b) with fixed a,c,d and variable l,b.
Step 4: Create a 3D surface plot of G(l,b).
Step 5: Display the 3D surface plot.

  

 
 

 

Download can_we_plotthisin_3Dshapemprimes5-5-2025.mw

How generate systems of equation and solve?...

Asked by: SSMB 100
coefficients conjugate duplicate-question
May 05 2025
2  3

in here How we can seperate the coefficent of conjugate this conjugate sign how remove from my equation ?

> 

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, t)); declare(U(xi)); declare(V(xi)); declare(P(x, t)); declare(q(x, t))

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

  

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

  

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

  

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

  

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

 (2)
> 

pde := I*(diff(u(x, t), t))+diff(u(x, t), `$`(x, 2))+abs(u(x, t))^2*u(x, t) = 0

I*(diff(u(x, t), t))+diff(diff(u(x, t), x), x)+abs(u(x, t))^2*u(x, t) = 0

 (3)
> 

S := u(x, t) = (sqrt(a)+P(x, t))*exp(I*a*t)

u(x, t) = (a^(1/2)+P(x, t))*exp(I*a*t)

 (4)
> 

S1 := conjugate(u(x, t)) = (sqrt(a)+conjugate(P(x, t)))*exp(-I*a*t)

conjugate(u(x, t)) = (a^(1/2)+conjugate(P(x, t)))*exp(-I*a*t)

 (5)
> 

Q := abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

abs(u(x, t))^2 = u(x, t)*conjugate(u(x, t))

 (6)
> 

F1 := expand(simplify(subs({S, S1}, rhs(Q))))

a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))+abs(P(x, t))^2

 (7)
> 

F2 := abs(u(x, t))^2 = remove(has, F1, abs(P(x, t))^2)

abs(u(x, t))^2 = a+a^(1/2)*P(x, t)+a^(1/2)*conjugate(P(x, t))

 (8)
> 

FF := collect(F2, sqrt(a))

abs(u(x, t))^2 = a+(P(x, t)+conjugate(P(x, t)))*a^(1/2)

 (9)
> 

F3 := abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*sqrt(a))*rhs(S)

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

 (10)
> 

F4 := remove(has, F3, P(x, t)*conjugate(P(x, t)))

abs(u(x, t))^2*u(x, t) = (a+(P(x, t)+conjugate(P(x, t)))*a^(1/2))*(a^(1/2)+P(x, t))*exp(I*a*t)

 (11)
> 

expand(%)

abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

 (12)
> 

pde_linear, pde_nonlinear := selectremove(proc (term) options operator, arrow; not has((eval(term, P(x, t) = T*P(x, t)))/T, T) end proc, expand(%))

() = (), abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a^(1/2)*P(x, t)^2+exp(I*a*t)*a*conjugate(P(x, t))+exp(I*a*t)*a^(1/2)*conjugate(P(x, t))*P(x, t)

 (13)
> 

F6 := abs(u(x, t))^2*u(x, t) = exp(I*a*t)*a^(3/2)+2*exp(I*a*t)*a*P(x, t)+exp(I*a*t)*a*conjugate(P(x, t))

abs(u(x, t))^2*u(x, t) = exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t))

 (14)
> 

subs({F6, S}, pde)

I*(diff((a^(1/2)+P(x, t))*exp(a*t*I), t))+diff(diff((a^(1/2)+P(x, t))*exp(a*t*I), x), x)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (15)
> 

eval(%)

I*((diff(P(x, t), t))*exp(a*t*I)+I*(a^(1/2)+P(x, t))*a*exp(a*t*I))+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a^(3/2)+2*exp(a*t*I)*a*P(x, t)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (16)
> 

expand(%)

I*(diff(P(x, t), t))*exp(a*t*I)+exp(a*t*I)*a*P(x, t)+(diff(diff(P(x, t), x), x))*exp(a*t*I)+exp(a*t*I)*a*conjugate(P(x, t)) = 0

 (17)
> 

expand(%/exp(I*a*t))

I*(diff(P(x, t), t))+a*P(x, t)+diff(diff(P(x, t), x), x)+a*conjugate(P(x, t)) = 0

 (18)
> 

PP := collect(%, a)

(P(x, t)+conjugate(P(x, t)))*a+I*(diff(P(x, t), t))+diff(diff(P(x, t), x), x) = 0

 (19)
> 

U1 := P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

P(x, t) = r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))

 (20)
> 

eval(subs(U1, PP))

(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0

 (21)
> 

simplify((r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))+conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t))))*a+I*(-I*r[1]*m*exp(I*(l*x-m*t))+I*r[2]*m*exp(-I*(l*x-m*t)))-r[1]*l^2*exp(I*(l*x-m*t))-r[2]*l^2*exp(-I*(l*x-m*t)) = 0)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

 (22)
> 

J := eval(%)

conjugate(r[1]*exp(I*(l*x-m*t))+r[2]*exp(-I*(l*x-m*t)))*a+r[2]*(-l^2+a-m)*exp(-I*(l*x-m*t))+r[1]*exp(I*(l*x-m*t))*(-l^2+a+m) = 0

 (23)
> 

expand(%)

a*conjugate(r[1])*exp(I*conjugate(m)*conjugate(t))/exp(I*conjugate(l)*conjugate(x))+a*conjugate(r[2])*exp(I*conjugate(l)*conjugate(x))/exp(I*conjugate(m)*conjugate(t))-r[2]*exp(I*m*t)*l^2/exp(I*l*x)+r[2]*exp(I*m*t)*a/exp(I*l*x)-r[2]*exp(I*m*t)*m/exp(I*l*x)-r[1]*exp(I*l*x)*l^2/exp(I*m*t)+r[1]*exp(I*l*x)*a/exp(I*m*t)+r[1]*exp(I*l*x)*m/exp(I*m*t) = 0

 (24)
> 

indets(%)

{a, l, m, t, x, r[1], r[2], exp(I*l*x), exp(I*m*t), exp(I*conjugate(l)*conjugate(x)), exp(I*conjugate(m)*conjugate(t)), conjugate(l), conjugate(m), conjugate(t), conjugate(x), conjugate(r[1]), conjugate(r[2])}

 (25)
> 

subs({exp(-I*(l*x-m*t)) = Y, exp(I*(l*x-m*t)) = X}, J)

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

 (26)
> 

collect(%, {X, Y})

conjugate(X*r[1]+Y*r[2])*a+r[2]*(-l^2+a-m)*Y+r[1]*X*(-l^2+a+m) = 0

 (27)

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Clarifying and Solving a New ODE with Exponential ...

Asked by: salim-barzani 1410
ode differential-equations duplicate-question
May 03 2025
1  10

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

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