Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Dear All,

I am facing some problems. This kind of error has been shown ""Error, (in plot/iplot2d/expression) bad range arguments 0.3e-1 = .1 .. .5, 0.3e-1 = .1 .. .5"

Error.mw

Hello,

With the new version 2025, double-clicking a file opens a second instance of Maple.

How can I make this open a new tab in the active instance, as it did with version 2024?

Thank you.

Bests regards.

I wanted to try this simplification in Maple 2025, only to find timelimit hangs.

Waited 3 hrs when timelimit was 30 second. It seems simplify got locked up and timelimit does not work.

Not only that, Maple itself hangs and clicking on retsrat kernel or red small bottom at lower level corner in Maple 2025 has no effect at all.  

Only way is to kill all of Maple from command line.

Make sure to save all your work before trying.

There are two bugs here: First is that timelimit still hangs (even though Maplesoft claimed it is fixed almost 5 years ago)

https://www.mapleprimes.com/maplesoftblog/213986-Introducing-Maple-Learn-officially

You will also be pleased to know that Maple 2021 addresses the timelimit() issue that you mentioned.

The second issue is that one can not close the kernel from frontend. (well, this is because kernel hanged)

Note that closing Maple works using File->EXIT but this leaves the Maple kernel/mserver  running  in background!

So had to go kill that process from command line manually also.

So make sure to do this, else you will end up with many mserver processes running in background after maple is closed if you try this more than one time.

Any one knows why this happens for this example? Should not timelimit have finally been fixed in Maple 2025?

I have been complaining about timelimit not always working for ages. Have no idea why Maplesoft can't figure solution to this problem for good. 

timelimit is the most important command for me, as without it, my program will never work and will just keep hanging.

I spend 50% of my time finding worarounds around Maple bugs instead of what I should be doing which is write more code.

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 1869. 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;

e:= -a*(-1/2*((1/2*x)^a)^4*(2^a)^4*_C8^4*a*x+1/2*((1/2*x)^a)^3*(2^a)^3*(((2^a)^2*((
1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8^3*x+1/4
*((1/2*x)^a)^2*(2^a)^2*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1
/2*x)^a)^2/_C8^2)^(1/2)*4^(1/2)*(x^2*(((1/2*x)^a)^4*(2^a)^4*_C8^4*a^2+(2^a)^4*(
(1/2*x)^a)^4*_C8^4+2*((1/2*x)^a)^2*(2^a)^2*_C8^2*a^4*b^2-2*((1/2*x)^a)^3*(2^a)^
3*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/
2)*_C8^3*a-4*a^2*b^2*(2^a)^2*((1/2*x)^a)^2*_C8^2+a^6*b^4-2*(1/2*x)^a*2^a*(((2^a
)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a
^3*b^2+2*b^2*(2^a)^2*((1/2*x)^a)^2*_C8^2-a^4*b^4+2*(1/2*x)^a*2^a*(((2^a)^2*((1/
2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a*b^2-a^2
*b^4+b^4)/(a-1)^2/(1+a)^2/_C8^2/((1/2*x)^a)^2/(2^a)^2)^(1/2)*_C8^2*a^2+1/2*a^5*
b^4*x-1/2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((
1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a^2*b^2*x-1/4*((1/2*x)^a)^2*(2^a)^2*(((2^a)^2*((1/
2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*4^(1/2)*(x^2*
(((1/2*x)^a)^4*(2^a)^4*_C8^4*a^2+(2^a)^4*((1/2*x)^a)^4*_C8^4+2*((1/2*x)^a)^2*(2
^a)^2*_C8^2*a^4*b^2-2*((1/2*x)^a)^3*(2^a)^3*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b
^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8^3*a-4*a^2*b^2*(2^a)^2*((1/2*x)
^a)^2*_C8^2+a^6*b^4-2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^
2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a^3*b^2+2*b^2*(2^a)^2*((1/2*x)^a)^2*
_C8^2-a^4*b^4+2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a
)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*a*b^2-a^2*b^4+b^4)/(a-1)^2/(1+a)^2/_C8^2/((1
/2*x)^a)^2/(2^a)^2)^(1/2)*_C8^2-a^3*b^4*x+1/2*(1/2*x)^a*2^a*(((2^a)^2*((1/2*x)^
a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1/2*x)^a)^2/_C8^2)^(1/2)*_C8*b^2*x+1/2*a*b^
4*x)/(a-1)/(1+a)/_C8^2/(((2^a)^2*((1/2*x)^a)^2*_C8^2-a^2*b^2+b^2)^2/(2^a)^2/((1
/2*x)^a)^2/_C8^2)^(1/2)/((1/2*x)^a)^2/(2^a)^2:

try
  timelimit(30, (simplify(e) assuming real)):
catch:
   print("cought timelimit");
end try:

 

 

Download timelimit_hang_in_maple_2025.mw

Hello,
Can you tell me how to decompose a rational fraction into simple elements in Fp?

Thank you.

I'm using an old old version of Maple (Maple 7) and there's a mistake in the Mellin Transform which hopefully has long since been fixed in subsequent versions but just in case it hasn't....

I was taking the Mellin Transform of Bessel Functions, specifically BesselK, and it's fine for BesselK(0,x), but when I compute BesselK(0,x^{1/2}), it gives the wrong answer.

In the transform of BesselK(0,x^(1/2)), It should be Gamma(p) not Gamma(p/2).

I'm not sure if this is fixed in newer Maples or if there's a work around. 

Whenever I size a 3d plot, that I'm trying to stretch out the width while keeping the height, never seems to work.  For example using the size=[3000,800] produces a plot area that's bigger but NOT actually a plot stretched in the x axis.  Going to size=[3000,3000] of course then makes the plot and the area bigger and so scales both x and y bigger.  However I don't want the y axis scaled up - I'm trying to scale the plot up - not the area.  And what happened to the window zoom, icon - we've lost zoom control to just magnify + and magnify - (at least in 2022) this seems like a regression. 

Is this plot size a bug or just a plot command that fails to function like it should? 

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

 

Hi, I'm new to Maple.

when nesting some multiplications in a summation operator, I get results that I can't figure out.

I've entered 4 formulas that should give the same result, if I understood things correctly. The formula FB gives me problems; am I doing something wrong, or is there a bug in Maple? The problem arose in a more complicated formula, but I trimmed the formula down to a minimum, in order to illustrate the discrepancy.

I hope someone can shed some light on this, because I'm stuck.

Is this a bug (the correct answer = 2)?

 

restart

 

FA := modp(5, product(2, t = 0 .. modp(1-1, 3)))+modp(5, product(2, t = 0 .. modp(2-1, 3))); FB := sum(modp(5, product(2, t = 0 .. modp(q-1, 3))), q = 1 .. 2)

10

(1)

FC := modp(5, product(2, t = 0 .. modp(0, 3)))+modp(5, product(2, t = 0 .. modp(1, 3))); FD := sum(modp(5, product(2, t = 0 .. modp(q, 3))), q = 0 .. 1)

2

(2)

NULL

FA := modp(5, product(2, t = 0 .. modp(1 - 1, 3))) + modp(5, product(2, t = 0 .. modp(2 - 1, 3)));

2

(3)

 

FB := sum(modp(5, product(2, t = 0 .. modp(q - 1, 3))), q = 1 .. 2);

10

(4)

 

FC := modp(5, product(2, t = 0 .. modp(0, 3))) + modp(5, product(2, t = 0 .. modp(1, 3)));

2

(5)

NULL

FD := sum(modp(5, product(2, t = 0 .. modp(q, 3))), q = 0 .. 1);

2

(6)

NULL

Download BugTestSimple.mw

How do I find the solutions "links" with only answers in the range 0 to +1? The domain of vgl is 0 <=beta <= 1. If the system is inconsistent or insufficient to solve xi (for example, if xi does not appear in the equation) then give the text "no solution". If there is a solution then show it. Filter only real solutions. Please help me with better code:

restart;
assume(beta > 0, beta < 1):
interface(showassumed=0):

vgl[1] := -((beta*xi^2 + 2*xi^2 - beta)*(beta - 1)^2)/4 = 0:  # or some other equation (sometimes xi does not appear in the equation)

if has(lhs(vgl[1]), xi) or has(rhs(vgl[1]), xi) then
    links := solve([vgl[1], xi > 0, xi < beta], xi):
    # Filter only real solutions
    links_real := select(x -> type(x, equation) and is(Im(rhs(x)) = 0), [links]):
    if nops(links_real) > 0 then
        x1 := links_real;
        print("Real solution(s):", x1);
    else
        print("No real solution in range for xi.");
    end if;
else
    print("The equation does not contain xi — solving for xi is not possible.");
end if;

 

I would like to automatically select a set of parameters that gives me a "good" solution, ideally, one where not all parameters are zero. The parameters A[0], A[1], A[2], B[1], and B[2] are essential and must always be included. The other parameters are optional and can be selected in various combinations (e.g., one, two, or more at a time).

Currently, I manually add or remove these optional parameters, which is time-consuming. I’m looking for a way to automate the selection process to find the best combination of parameters that yields a valid and meaningful (non-zero) solution.

How can I approach this systematically?

params.mw

restart

with(PDEtools)

with(LinearAlgebra)

NULL

with(SolveTools)

with(LargeExpressions)

undeclare(prime)

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

(1)

declare(u(x, t), quiet); declare(V(xi), quiet); declare(U(xi), quiet)

NULL

CoefficientNullity := [0 = k^3*(beta*s-w)*(A[0]+A[1]+A[2]+B[1]+B[2])*(-5*beta*s*A[0]^2*c[2]-10*beta*s*A[0]*A[1]*c[2]-10*beta*s*A[0]*A[2]*c[2]-10*beta*s*A[0]*B[1]*c[2]-10*beta*s*A[0]*B[2]*c[2]-5*beta*s*A[1]^2*c[2]-10*beta*s*A[1]*A[2]*c[2]-10*beta*s*A[1]*B[1]*c[2]-10*beta*s*A[1]*B[2]*c[2]-5*beta*s*A[2]^2*c[2]-10*beta*s*A[2]*B[1]*c[2]-10*beta*s*A[2]*B[2]*c[2]-5*beta*s*B[1]^2*c[2]-10*beta*s*B[1]*B[2]*c[2]-5*beta*s*B[2]^2*c[2]+3*beta*k*s*w+5*w*A[0]^2*c[2]+10*w*A[0]*A[1]*c[2]+10*w*A[0]*A[2]*c[2]+10*w*A[0]*B[1]*c[2]+10*w*A[0]*B[2]*c[2]+5*w*A[1]^2*c[2]+10*w*A[1]*A[2]*c[2]+10*w*A[1]*B[1]*c[2]+10*w*A[1]*B[2]*c[2]+5*w*A[2]^2*c[2]+10*w*A[2]*B[1]*c[2]+10*w*A[2]*B[2]*c[2]+5*w*B[1]^2*c[2]+10*w*B[1]*B[2]*c[2]+5*w*B[2]^2*c[2]+2*k*s^2-5*k*w^2), 0 = (beta*s-w)*(5*beta*k^3*s*A[0]^3*c[2]-15*beta*k^3*s*A[0]^2*A[1]*c[2]-45*beta*k^3*s*A[0]^2*A[2]*c[2]+45*beta*k^3*s*A[0]^2*B[1]*c[2]+45*beta*k^3*s*A[0]^2*B[2]*c[2]-45*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+30*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+30*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*A[2]^2*c[2]-30*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+75*beta*k^3*s*A[0]*B[1]^2*c[2]+150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]-105*beta*k^3*s*A[1]^2*A[2]*c[2]-15*beta*k^3*s*A[1]^2*B[1]*c[2]-15*beta*k^3*s*A[1]^2*B[2]*c[2]-135*beta*k^3*s*A[1]*A[2]^2*c[2]-90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[1]^2*c[2]+90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[2]^2*c[2]-55*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]+15*beta*k^3*s*A[2]*B[1]^2*c[2]+30*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[2]*B[2]^2*c[2]+35*beta*k^3*s*B[1]^3*c[2]+105*beta*k^3*s*B[1]^2*B[2]*c[2]+105*beta*k^3*s*B[1]*B[2]^2*c[2]+35*beta*k^3*s*B[2]^3*c[2]-3*beta*k^4*s*w*A[0]+3*beta*k^4*s*w*A[1]+9*beta*k^4*s*w*A[2]-9*beta*k^4*s*w*B[1]-9*beta*k^4*s*w*B[2]-5*k^3*w*A[0]^3*c[2]+15*k^3*w*A[0]^2*A[1]*c[2]+45*k^3*w*A[0]^2*A[2]*c[2]-45*k^3*w*A[0]^2*B[1]*c[2]-45*k^3*w*A[0]^2*B[2]*c[2]+45*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]-30*k^3*w*A[0]*A[1]*B[1]*c[2]-30*k^3*w*A[0]*A[1]*B[2]*c[2]+105*k^3*w*A[0]*A[2]^2*c[2]+30*k^3*w*A[0]*A[2]*B[1]*c[2]+30*k^3*w*A[0]*A[2]*B[2]*c[2]-75*k^3*w*A[0]*B[1]^2*c[2]-150*k^3*w*A[0]*B[1]*B[2]*c[2]-75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]+105*k^3*w*A[1]^2*A[2]*c[2]+15*k^3*w*A[1]^2*B[1]*c[2]+15*k^3*w*A[1]^2*B[2]*c[2]+135*k^3*w*A[1]*A[2]^2*c[2]+90*k^3*w*A[1]*A[2]*B[1]*c[2]+90*k^3*w*A[1]*A[2]*B[2]*c[2]-45*k^3*w*A[1]*B[1]^2*c[2]-90*k^3*w*A[1]*B[1]*B[2]*c[2]-45*k^3*w*A[1]*B[2]^2*c[2]+55*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]-15*k^3*w*A[2]*B[1]^2*c[2]-30*k^3*w*A[2]*B[1]*B[2]*c[2]-15*k^3*w*A[2]*B[2]^2*c[2]-35*k^3*w*B[1]^3*c[2]-105*k^3*w*B[1]^2*B[2]*c[2]-105*k^3*w*B[1]*B[2]^2*c[2]-35*k^3*w*B[2]^3*c[2]+40*beta^2*k^2*s^2*A[1]+80*beta^2*k^2*s^2*A[2]-40*beta^2*k^2*s^2*B[1]-40*beta^2*k^2*s^2*B[2]-2*k^4*s^2*A[0]+2*k^4*s^2*A[1]+6*k^4*s^2*A[2]-6*k^4*s^2*B[1]-6*k^4*s^2*B[2]+5*k^4*w^2*A[0]-5*k^4*w^2*A[1]-15*k^4*w^2*A[2]+15*k^4*w^2*B[1]+15*k^4*w^2*B[2]-80*beta*k^2*s*w*A[1]-160*beta*k^2*s*w*A[2]+80*beta*k^2*s*w*B[1]+80*beta*k^2*s*w*B[2]+40*k^2*s^2*A[1]+80*k^2*s^2*A[2]-40*k^2*s^2*B[1]-40*k^2*s^2*B[2]-160*beta*s*w*A[1]-320*beta*s*w*A[2]+160*beta*s*w*B[1]+160*beta*s*w*B[2]+160*s^2*A[1]+320*s^2*A[2]-160*s^2*B[1]-160*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+15*beta*k^3*s*A[0]^2*A[2]*c[2]+15*beta*k^3*s*A[0]^2*B[1]*c[2]+15*beta*k^3*s*A[0]^2*B[2]*c[2]+15*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-285*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[1]^2*c[2]-210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]-285*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-525*beta*k^3*s*A[1]*A[2]^2*c[2]+30*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+30*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[1]^2*c[2]+30*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[2]^2*c[2]-275*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]-95*beta*k^3*s*B[1]^3*c[2]-285*beta*k^3*s*B[1]^2*B[2]*c[2]-285*beta*k^3*s*B[1]*B[2]^2*c[2]-95*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-3*beta*k^4*s*w*A[2]-3*beta*k^4*s*w*B[1]-3*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-15*k^3*w*A[0]^2*A[2]*c[2]-15*k^3*w*A[0]^2*B[1]*c[2]-15*k^3*w*A[0]^2*B[2]*c[2]-15*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]+285*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+105*k^3*w*A[0]*B[1]^2*c[2]+210*k^3*w*A[0]*B[1]*B[2]*c[2]+105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]+285*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+525*k^3*w*A[1]*A[2]^2*c[2]-30*k^3*w*A[1]*A[2]*B[1]*c[2]-30*k^3*w*A[1]*A[2]*B[2]*c[2]-15*k^3*w*A[1]*B[1]^2*c[2]-30*k^3*w*A[1]*B[1]*B[2]*c[2]-15*k^3*w*A[1]*B[2]^2*c[2]+275*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]+95*k^3*w*B[1]^3*c[2]+285*k^3*w*B[1]^2*B[2]*c[2]+285*k^3*w*B[1]*B[2]^2*c[2]+95*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]+560*beta^2*k^2*s^2*A[2]+200*beta^2*k^2*s^2*B[1]+200*beta^2*k^2*s^2*B[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-2*k^4*s^2*A[2]-2*k^4*s^2*B[1]-2*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+5*k^4*w^2*A[2]+5*k^4*w^2*B[1]+5*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]-1120*beta*k^2*s*w*A[2]-400*beta*k^2*s*w*B[1]-400*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]+560*k^2*s^2*A[2]+200*k^2*s^2*B[1]+200*k^2*s^2*B[2]-2400*beta*s*w*A[1]-9920*beta*s*w*A[2]-2720*beta*s*w*B[1]-2720*beta*s*w*B[2]+2400*s^2*A[1]+9920*s^2*A[2]+2720*s^2*B[1]+2720*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+165*beta*k^3*s*A[0]^2*A[2]*c[2]-165*beta*k^3*s*A[0]^2*B[1]*c[2]-165*beta*k^3*s*A[0]^2*B[2]*c[2]+165*beta*k^3*s*A[0]*A[1]^2*c[2]+150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]+25*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-1125*beta*k^3*s*A[1]*A[2]^2*c[2]+330*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+330*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-165*beta*k^3*s*A[1]*B[1]^2*c[2]-330*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-165*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]+75*beta*k^3*s*A[2]^2*B[1]*c[2]+75*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-33*beta*k^4*s*w*A[2]+33*beta*k^4*s*w*B[1]+33*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-165*k^3*w*A[0]^2*A[2]*c[2]+165*k^3*w*A[0]^2*B[1]*c[2]+165*k^3*w*A[0]^2*B[2]*c[2]-165*k^3*w*A[0]*A[1]^2*c[2]-150*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]-25*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+1125*k^3*w*A[1]*A[2]^2*c[2]-330*k^3*w*A[1]*A[2]*B[1]*c[2]-330*k^3*w*A[1]*A[2]*B[2]*c[2]+165*k^3*w*A[1]*B[1]^2*c[2]+330*k^3*w*A[1]*B[1]*B[2]*c[2]+165*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]-75*k^3*w*A[2]^2*B[1]*c[2]-75*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+1120*beta^2*k^2*s^2*A[2]-320*beta^2*k^2*s^2*B[1]-320*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-22*k^4*s^2*A[2]+22*k^4*s^2*B[1]+22*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+55*k^4*w^2*A[2]-55*k^4*w^2*B[1]-55*k^4*w^2*B[2]-2240*beta*k^2*s*w*A[2]+640*beta*k^2*s*w*B[1]+640*beta*k^2*s*w*B[2]+1120*k^2*s^2*A[2]-320*k^2*s^2*B[1]-320*k^2*s^2*B[2]-9600*beta*s*w*A[1]-65920*beta*s*w*A[2]+14720*beta*s*w*B[1]+14720*beta*s*w*B[2]+9600*s^2*A[1]+65920*s^2*A[2]-14720*s^2*B[1]-14720*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-45*beta*k^3*s*A[0]^2*A[2]*c[2]-45*beta*k^3*s*A[0]^2*B[1]*c[2]-45*beta*k^3*s*A[0]^2*B[2]*c[2]-45*beta*k^3*s*A[0]*A[1]^2*c[2]-330*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-45*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-165*beta*k^3*s*A[0]*B[1]^2*c[2]-330*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-165*beta*k^3*s*A[0]*B[2]^2*c[2]-55*beta*k^3*s*A[1]^3*c[2]-45*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+675*beta*k^3*s*A[1]*A[2]^2*c[2]-90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[1]^2*c[2]-90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[2]^2*c[2]+825*beta*k^3*s*A[2]^3*c[2]-165*beta*k^3*s*A[2]^2*B[1]*c[2]-165*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]-15*beta*k^3*s*B[1]^3*c[2]-45*beta*k^3*s*B[1]^2*B[2]*c[2]-45*beta*k^3*s*B[1]*B[2]^2*c[2]-15*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+9*beta*k^4*s*w*A[2]+9*beta*k^4*s*w*B[1]+9*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+45*k^3*w*A[0]^2*A[2]*c[2]+45*k^3*w*A[0]^2*B[1]*c[2]+45*k^3*w*A[0]^2*B[2]*c[2]+45*k^3*w*A[0]*A[1]^2*c[2]+330*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]+45*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+165*k^3*w*A[0]*B[1]^2*c[2]+330*k^3*w*A[0]*B[1]*B[2]*c[2]+165*k^3*w*A[0]*B[2]^2*c[2]+55*k^3*w*A[1]^3*c[2]+45*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-675*k^3*w*A[1]*A[2]^2*c[2]+90*k^3*w*A[1]*A[2]*B[1]*c[2]+90*k^3*w*A[1]*A[2]*B[2]*c[2]+45*k^3*w*A[1]*B[1]^2*c[2]+90*k^3*w*A[1]*B[1]*B[2]*c[2]+45*k^3*w*A[1]*B[2]^2*c[2]-825*k^3*w*A[2]^3*c[2]+165*k^3*w*A[2]^2*B[1]*c[2]+165*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]+15*k^3*w*B[1]^3*c[2]+45*k^3*w*B[1]^2*B[2]*c[2]+45*k^3*w*B[1]*B[2]^2*c[2]+15*k^3*w*B[2]^3*c[2]+160*beta^2*k^2*s^2*A[1]-80*beta^2*k^2*s^2*A[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+6*k^4*s^2*A[2]+6*k^4*s^2*B[1]+6*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-15*k^4*w^2*A[2]-15*k^4*w^2*B[1]-15*k^4*w^2*B[2]-320*beta*k^2*s*w*A[1]+160*beta*k^2*s*w*A[2]+160*k^2*s^2*A[1]-80*k^2*s^2*A[2]+8000*beta*s*w*A[1]+100160*beta*s*w*A[2]+20160*beta*s*w*B[1]+20160*beta*s*w*B[2]-8000*s^2*A[1]-100160*s^2*A[2]-20160*s^2*B[1]-20160*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+105*beta*k^3*s*A[0]^2*A[2]*c[2]-105*beta*k^3*s*A[0]^2*B[1]*c[2]-105*beta*k^3*s*A[0]^2*B[2]*c[2]+105*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[1]^2*c[2]+210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+315*beta*k^3*s*A[1]*A[2]^2*c[2]+210*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+210*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[1]^2*c[2]-210*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[2]^2*c[2]+1155*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-21*beta*k^4*s*w*A[2]+21*beta*k^4*s*w*B[1]+21*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-105*k^3*w*A[0]^2*A[2]*c[2]+105*k^3*w*A[0]^2*B[1]*c[2]+105*k^3*w*A[0]^2*B[2]*c[2]-105*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-105*k^3*w*A[0]*B[1]^2*c[2]-210*k^3*w*A[0]*B[1]*B[2]*c[2]-105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-315*k^3*w*A[1]*A[2]^2*c[2]-210*k^3*w*A[1]*A[2]*B[1]*c[2]-210*k^3*w*A[1]*A[2]*B[2]*c[2]+105*k^3*w*A[1]*B[1]^2*c[2]+210*k^3*w*A[1]*B[1]*B[2]*c[2]+105*k^3*w*A[1]*B[2]^2*c[2]-1155*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]+960*beta^2*k^2*s^2*A[2]-280*beta^2*k^2*s^2*B[1]-280*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-14*k^4*s^2*A[2]+14*k^4*s^2*B[1]+14*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+35*k^4*w^2*A[2]-35*k^4*w^2*B[1]-35*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]-1920*beta*k^2*s*w*A[2]+560*beta*k^2*s*w*B[1]+560*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]+960*k^2*s^2*A[2]-280*k^2*s^2*B[1]-280*k^2*s^2*B[2]+4320*beta*s*w*A[1]+168960*beta*s*w*A[2]-32480*beta*s*w*B[1]-32480*beta*s*w*B[2]-4320*s^2*A[1]-168960*s^2*A[2]+32480*s^2*B[1]+32480*s^2*B[2]), 0 = (beta*s-w)*(25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-105*beta*k^3*s*A[0]^2*A[2]*c[2]-105*beta*k^3*s*A[0]^2*B[1]*c[2]-105*beta*k^3*s*A[0]^2*B[2]*c[2]-105*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+315*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[1]^2*c[2]-210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]+315*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+315*beta*k^3*s*A[1]*A[2]^2*c[2]-210*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-210*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[1]^2*c[2]-210*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-105*beta*k^3*s*A[1]*B[2]^2*c[2]-1155*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]+75*beta*k^3*s*A[2]*B[1]^2*c[2]+150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]+75*beta*k^3*s*A[2]*B[2]^2*c[2]+105*beta*k^3*s*B[1]^3*c[2]+315*beta*k^3*s*B[1]^2*B[2]*c[2]+315*beta*k^3*s*B[1]*B[2]^2*c[2]+105*beta*k^3*s*B[2]^3*c[2]-15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+21*beta*k^4*s*w*A[2]+21*beta*k^4*s*w*B[1]+21*beta*k^4*s*w*B[2]-25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+105*k^3*w*A[0]^2*A[2]*c[2]+105*k^3*w*A[0]^2*B[1]*c[2]+105*k^3*w*A[0]^2*B[2]*c[2]+105*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]-150*k^3*w*A[0]*A[1]*B[1]*c[2]-150*k^3*w*A[0]*A[1]*B[2]*c[2]-315*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]+105*k^3*w*A[0]*B[1]^2*c[2]+210*k^3*w*A[0]*B[1]*B[2]*c[2]+105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]-315*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-315*k^3*w*A[1]*A[2]^2*c[2]+210*k^3*w*A[1]*A[2]*B[1]*c[2]+210*k^3*w*A[1]*A[2]*B[2]*c[2]+105*k^3*w*A[1]*B[1]^2*c[2]+210*k^3*w*A[1]*B[1]*B[2]*c[2]+105*k^3*w*A[1]*B[2]^2*c[2]+1155*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]-75*k^3*w*A[2]*B[1]^2*c[2]-150*k^3*w*A[2]*B[1]*B[2]*c[2]-75*k^3*w*A[2]*B[2]^2*c[2]-105*k^3*w*B[1]^3*c[2]-315*k^3*w*B[1]^2*B[2]*c[2]-315*k^3*w*B[1]*B[2]^2*c[2]-105*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]-960*beta^2*k^2*s^2*A[2]-280*beta^2*k^2*s^2*B[1]-280*beta^2*k^2*s^2*B[2]-10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+14*k^4*s^2*A[2]+14*k^4*s^2*B[1]+14*k^4*s^2*B[2]+25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-35*k^4*w^2*A[2]-35*k^4*w^2*B[1]-35*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]+1920*beta*k^2*s*w*A[2]+560*beta*k^2*s*w*B[1]+560*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]-960*k^2*s^2*A[2]-280*k^2*s^2*B[1]-280*k^2*s^2*B[2]+4320*beta*s*w*A[1]-168960*beta*s*w*A[2]-32480*beta*s*w*B[1]-32480*beta*s*w*B[2]-4320*s^2*A[1]+168960*s^2*A[2]+32480*s^2*B[1]+32480*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]+45*beta*k^3*s*A[0]^2*A[2]*c[2]-45*beta*k^3*s*A[0]^2*B[1]*c[2]-45*beta*k^3*s*A[0]^2*B[2]*c[2]+45*beta*k^3*s*A[0]*A[1]^2*c[2]-330*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+45*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+165*beta*k^3*s*A[0]*B[1]^2*c[2]+330*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+165*beta*k^3*s*A[0]*B[2]^2*c[2]-55*beta*k^3*s*A[1]^3*c[2]+45*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]+675*beta*k^3*s*A[1]*A[2]^2*c[2]+90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[1]^2*c[2]-90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]-45*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]-165*beta*k^3*s*A[2]^2*B[1]*c[2]-165*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-15*beta*k^3*s*B[1]^3*c[2]-45*beta*k^3*s*B[1]^2*B[2]*c[2]-45*beta*k^3*s*B[1]*B[2]^2*c[2]-15*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]-9*beta*k^4*s*w*A[2]+9*beta*k^4*s*w*B[1]+9*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]-45*k^3*w*A[0]^2*A[2]*c[2]+45*k^3*w*A[0]^2*B[1]*c[2]+45*k^3*w*A[0]^2*B[2]*c[2]-45*k^3*w*A[0]*A[1]^2*c[2]+330*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]-45*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-165*k^3*w*A[0]*B[1]^2*c[2]-330*k^3*w*A[0]*B[1]*B[2]*c[2]-165*k^3*w*A[0]*B[2]^2*c[2]+55*k^3*w*A[1]^3*c[2]-45*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]-675*k^3*w*A[1]*A[2]^2*c[2]-90*k^3*w*A[1]*A[2]*B[1]*c[2]-90*k^3*w*A[1]*A[2]*B[2]*c[2]+45*k^3*w*A[1]*B[1]^2*c[2]+90*k^3*w*A[1]*B[1]*B[2]*c[2]+45*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]+165*k^3*w*A[2]^2*B[1]*c[2]+165*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+15*k^3*w*B[1]^3*c[2]+45*k^3*w*B[1]^2*B[2]*c[2]+45*k^3*w*B[1]*B[2]^2*c[2]+15*k^3*w*B[2]^3*c[2]+160*beta^2*k^2*s^2*A[1]+80*beta^2*k^2*s^2*A[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]-6*k^4*s^2*A[2]+6*k^4*s^2*B[1]+6*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]+15*k^4*w^2*A[2]-15*k^4*w^2*B[1]-15*k^4*w^2*B[2]-320*beta*k^2*s*w*A[1]-160*beta*k^2*s*w*A[2]+160*k^2*s^2*A[1]+80*k^2*s^2*A[2]+8000*beta*s*w*A[1]-100160*beta*s*w*A[2]+20160*beta*s*w*B[1]+20160*beta*s*w*B[2]-8000*s^2*A[1]+100160*s^2*A[2]-20160*s^2*B[1]-20160*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]-75*beta*k^3*s*A[0]^2*A[1]*c[2]+165*beta*k^3*s*A[0]^2*A[2]*c[2]+165*beta*k^3*s*A[0]^2*B[1]*c[2]+165*beta*k^3*s*A[0]^2*B[2]*c[2]+165*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]-315*beta*k^3*s*A[0]*A[2]^2*c[2]-150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]-315*beta*k^3*s*A[1]^2*A[2]*c[2]-75*beta*k^3*s*A[1]^2*B[1]*c[2]-75*beta*k^3*s*A[1]^2*B[2]*c[2]+1125*beta*k^3*s*A[1]*A[2]^2*c[2]+330*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+330*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+165*beta*k^3*s*A[1]*B[1]^2*c[2]+330*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+165*beta*k^3*s*A[1]*B[2]^2*c[2]-825*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-105*beta*k^3*s*B[1]^3*c[2]-315*beta*k^3*s*B[1]^2*B[2]*c[2]-315*beta*k^3*s*B[1]*B[2]^2*c[2]-105*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]+15*beta*k^4*s*w*A[1]-33*beta*k^4*s*w*A[2]-33*beta*k^4*s*w*B[1]-33*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]+75*k^3*w*A[0]^2*A[1]*c[2]-165*k^3*w*A[0]^2*A[2]*c[2]-165*k^3*w*A[0]^2*B[1]*c[2]-165*k^3*w*A[0]^2*B[2]*c[2]-165*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]+315*k^3*w*A[0]*A[2]^2*c[2]+150*k^3*w*A[0]*A[2]*B[1]*c[2]+150*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]+315*k^3*w*A[1]^2*A[2]*c[2]+75*k^3*w*A[1]^2*B[1]*c[2]+75*k^3*w*A[1]^2*B[2]*c[2]-1125*k^3*w*A[1]*A[2]^2*c[2]-330*k^3*w*A[1]*A[2]*B[1]*c[2]-330*k^3*w*A[1]*A[2]*B[2]*c[2]-165*k^3*w*A[1]*B[1]^2*c[2]-330*k^3*w*A[1]*B[1]*B[2]*c[2]-165*k^3*w*A[1]*B[2]^2*c[2]+825*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+105*k^3*w*B[1]^3*c[2]+315*k^3*w*B[1]^2*B[2]*c[2]+315*k^3*w*B[1]*B[2]^2*c[2]+105*k^3*w*B[2]^3*c[2]+1120*beta^2*k^2*s^2*A[2]+320*beta^2*k^2*s^2*B[1]+320*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]+10*k^4*s^2*A[1]-22*k^4*s^2*A[2]-22*k^4*s^2*B[1]-22*k^4*s^2*B[2]-25*k^4*w^2*A[0]-25*k^4*w^2*A[1]+55*k^4*w^2*A[2]+55*k^4*w^2*B[1]+55*k^4*w^2*B[2]-2240*beta*k^2*s*w*A[2]-640*beta*k^2*s*w*B[1]-640*beta*k^2*s*w*B[2]+1120*k^2*s^2*A[2]+320*k^2*s^2*B[1]+320*k^2*s^2*B[2]+9600*beta*s*w*A[1]-65920*beta*s*w*A[2]-14720*beta*s*w*B[1]-14720*beta*s*w*B[2]-9600*s^2*A[1]+65920*s^2*A[2]+14720*s^2*B[1]+14720*s^2*B[2]), 0 = (beta*s-w)*(-25*beta*k^3*s*A[0]^3*c[2]+75*beta*k^3*s*A[0]^2*A[1]*c[2]-15*beta*k^3*s*A[0]^2*A[2]*c[2]+15*beta*k^3*s*A[0]^2*B[1]*c[2]+15*beta*k^3*s*A[0]^2*B[2]*c[2]-15*beta*k^3*s*A[0]*A[1]^2*c[2]-210*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-150*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+285*beta*k^3*s*A[0]*A[2]^2*c[2]+150*beta*k^3*s*A[0]*A[2]*B[1]*c[2]+150*beta*k^3*s*A[0]*A[2]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[1]^2*c[2]+210*beta*k^3*s*A[0]*B[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*B[2]^2*c[2]-35*beta*k^3*s*A[1]^3*c[2]+285*beta*k^3*s*A[1]^2*A[2]*c[2]+75*beta*k^3*s*A[1]^2*B[1]*c[2]+75*beta*k^3*s*A[1]^2*B[2]*c[2]-525*beta*k^3*s*A[1]*A[2]^2*c[2]-30*beta*k^3*s*A[1]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[1]^2*c[2]+30*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+15*beta*k^3*s*A[1]*B[2]^2*c[2]+275*beta*k^3*s*A[2]^3*c[2]-105*beta*k^3*s*A[2]^2*B[1]*c[2]-105*beta*k^3*s*A[2]^2*B[2]*c[2]-75*beta*k^3*s*A[2]*B[1]^2*c[2]-150*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[2]*B[2]^2*c[2]-95*beta*k^3*s*B[1]^3*c[2]-285*beta*k^3*s*B[1]^2*B[2]*c[2]-285*beta*k^3*s*B[1]*B[2]^2*c[2]-95*beta*k^3*s*B[2]^3*c[2]+15*beta*k^4*s*w*A[0]-15*beta*k^4*s*w*A[1]+3*beta*k^4*s*w*A[2]-3*beta*k^4*s*w*B[1]-3*beta*k^4*s*w*B[2]+25*k^3*w*A[0]^3*c[2]-75*k^3*w*A[0]^2*A[1]*c[2]+15*k^3*w*A[0]^2*A[2]*c[2]-15*k^3*w*A[0]^2*B[1]*c[2]-15*k^3*w*A[0]^2*B[2]*c[2]+15*k^3*w*A[0]*A[1]^2*c[2]+210*k^3*w*A[0]*A[1]*A[2]*c[2]+150*k^3*w*A[0]*A[1]*B[1]*c[2]+150*k^3*w*A[0]*A[1]*B[2]*c[2]-285*k^3*w*A[0]*A[2]^2*c[2]-150*k^3*w*A[0]*A[2]*B[1]*c[2]-150*k^3*w*A[0]*A[2]*B[2]*c[2]-105*k^3*w*A[0]*B[1]^2*c[2]-210*k^3*w*A[0]*B[1]*B[2]*c[2]-105*k^3*w*A[0]*B[2]^2*c[2]+35*k^3*w*A[1]^3*c[2]-285*k^3*w*A[1]^2*A[2]*c[2]-75*k^3*w*A[1]^2*B[1]*c[2]-75*k^3*w*A[1]^2*B[2]*c[2]+525*k^3*w*A[1]*A[2]^2*c[2]+30*k^3*w*A[1]*A[2]*B[1]*c[2]+30*k^3*w*A[1]*A[2]*B[2]*c[2]-15*k^3*w*A[1]*B[1]^2*c[2]-30*k^3*w*A[1]*B[1]*B[2]*c[2]-15*k^3*w*A[1]*B[2]^2*c[2]-275*k^3*w*A[2]^3*c[2]+105*k^3*w*A[2]^2*B[1]*c[2]+105*k^3*w*A[2]^2*B[2]*c[2]+75*k^3*w*A[2]*B[1]^2*c[2]+150*k^3*w*A[2]*B[1]*B[2]*c[2]+75*k^3*w*A[2]*B[2]^2*c[2]+95*k^3*w*B[1]^3*c[2]+285*k^3*w*B[1]^2*B[2]*c[2]+285*k^3*w*B[1]*B[2]^2*c[2]+95*k^3*w*B[2]^3*c[2]+120*beta^2*k^2*s^2*A[1]-560*beta^2*k^2*s^2*A[2]+200*beta^2*k^2*s^2*B[1]+200*beta^2*k^2*s^2*B[2]+10*k^4*s^2*A[0]-10*k^4*s^2*A[1]+2*k^4*s^2*A[2]-2*k^4*s^2*B[1]-2*k^4*s^2*B[2]-25*k^4*w^2*A[0]+25*k^4*w^2*A[1]-5*k^4*w^2*A[2]+5*k^4*w^2*B[1]+5*k^4*w^2*B[2]-240*beta*k^2*s*w*A[1]+1120*beta*k^2*s*w*A[2]-400*beta*k^2*s*w*B[1]-400*beta*k^2*s*w*B[2]+120*k^2*s^2*A[1]-560*k^2*s^2*A[2]+200*k^2*s^2*B[1]+200*k^2*s^2*B[2]-2400*beta*s*w*A[1]+9920*beta*s*w*A[2]-2720*beta*s*w*B[1]-2720*beta*s*w*B[2]+2400*s^2*A[1]-9920*s^2*A[2]+2720*s^2*B[1]+2720*s^2*B[2]), 0 = (beta*s-w)*(-5*beta*k^3*s*A[0]^3*c[2]-15*beta*k^3*s*A[0]^2*A[1]*c[2]+45*beta*k^3*s*A[0]^2*A[2]*c[2]+45*beta*k^3*s*A[0]^2*B[1]*c[2]+45*beta*k^3*s*A[0]^2*B[2]*c[2]+45*beta*k^3*s*A[0]*A[1]^2*c[2]-150*beta*k^3*s*A[0]*A[1]*A[2]*c[2]-30*beta*k^3*s*A[0]*A[1]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[1]*B[2]*c[2]+105*beta*k^3*s*A[0]*A[2]^2*c[2]-30*beta*k^3*s*A[0]*A[2]*B[1]*c[2]-30*beta*k^3*s*A[0]*A[2]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[1]^2*c[2]-150*beta*k^3*s*A[0]*B[1]*B[2]*c[2]-75*beta*k^3*s*A[0]*B[2]^2*c[2]-25*beta*k^3*s*A[1]^3*c[2]+105*beta*k^3*s*A[1]^2*A[2]*c[2]-15*beta*k^3*s*A[1]^2*B[1]*c[2]-15*beta*k^3*s*A[1]^2*B[2]*c[2]-135*beta*k^3*s*A[1]*A[2]^2*c[2]+90*beta*k^3*s*A[1]*A[2]*B[1]*c[2]+90*beta*k^3*s*A[1]*A[2]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[1]^2*c[2]+90*beta*k^3*s*A[1]*B[1]*B[2]*c[2]+45*beta*k^3*s*A[1]*B[2]^2*c[2]+55*beta*k^3*s*A[2]^3*c[2]-75*beta*k^3*s*A[2]^2*B[1]*c[2]-75*beta*k^3*s*A[2]^2*B[2]*c[2]-15*beta*k^3*s*A[2]*B[1]^2*c[2]-30*beta*k^3*s*A[2]*B[1]*B[2]*c[2]-15*beta*k^3*s*A[2]*B[2]^2*c[2]+35*beta*k^3*s*B[1]^3*c[2]+105*beta*k^3*s*B[1]^2*B[2]*c[2]+105*beta*k^3*s*B[1]*B[2]^2*c[2]+35*beta*k^3*s*B[2]^3*c[2]+3*beta*k^4*s*w*A[0]+3*beta*k^4*s*w*A[1]-9*beta*k^4*s*w*A[2]-9*beta*k^4*s*w*B[1]-9*beta*k^4*s*w*B[2]+5*k^3*w*A[0]^3*c[2]+15*k^3*w*A[0]^2*A[1]*c[2]-45*k^3*w*A[0]^2*A[2]*c[2]-45*k^3*w*A[0]^2*B[1]*c[2]-45*k^3*w*A[0]^2*B[2]*c[2]-45*k^3*w*A[0]*A[1]^2*c[2]+150*k^3*w*A[0]*A[1]*A[2]*c[2]+30*k^3*w*A[0]*A[1]*B[1]*c[2]+30*k^3*w*A[0]*A[1]*B[2]*c[2]-105*k^3*w*A[0]*A[2]^2*c[2]+30*k^3*w*A[0]*A[2]*B[1]*c[2]+30*k^3*w*A[0]*A[2]*B[2]*c[2]+75*k^3*w*A[0]*B[1]^2*c[2]+150*k^3*w*A[0]*B[1]*B[2]*c[2]+75*k^3*w*A[0]*B[2]^2*c[2]+25*k^3*w*A[1]^3*c[2]-105*k^3*w*A[1]^2*A[2]*c[2]+15*k^3*w*A[1]^2*B[1]*c[2]+15*k^3*w*A[1]^2*B[2]*c[2]+135*k^3*w*A[1]*A[2]^2*c[2]-90*k^3*w*A[1]*A[2]*B[1]*c[2]-90*k^3*w*A[1]*A[2]*B[2]*c[2]-45*k^3*w*A[1]*B[1]^2*c[2]-90*k^3*w*A[1]*B[1]*B[2]*c[2]-45*k^3*w*A[1]*B[2]^2*c[2]-55*k^3*w*A[2]^3*c[2]+75*k^3*w*A[2]^2*B[1]*c[2]+75*k^3*w*A[2]^2*B[2]*c[2]+15*k^3*w*A[2]*B[1]^2*c[2]+30*k^3*w*A[2]*B[1]*B[2]*c[2]+15*k^3*w*A[2]*B[2]^2*c[2]-35*k^3*w*B[1]^3*c[2]-105*k^3*w*B[1]^2*B[2]*c[2]-105*k^3*w*B[1]*B[2]^2*c[2]-35*k^3*w*B[2]^3*c[2]+40*beta^2*k^2*s^2*A[1]-80*beta^2*k^2*s^2*A[2]-40*beta^2*k^2*s^2*B[1]-40*beta^2*k^2*s^2*B[2]+2*k^4*s^2*A[0]+2*k^4*s^2*A[1]-6*k^4*s^2*A[2]-6*k^4*s^2*B[1]-6*k^4*s^2*B[2]-5*k^4*w^2*A[0]-5*k^4*w^2*A[1]+15*k^4*w^2*A[2]+15*k^4*w^2*B[1]+15*k^4*w^2*B[2]-80*beta*k^2*s*w*A[1]+160*beta*k^2*s*w*A[2]+80*beta*k^2*s*w*B[1]+80*beta*k^2*s*w*B[2]+40*k^2*s^2*A[1]-80*k^2*s^2*A[2]-40*k^2*s^2*B[1]-40*k^2*s^2*B[2]-160*beta*s*w*A[1]+320*beta*s*w*A[2]+160*beta*s*w*B[1]+160*beta*s*w*B[2]+160*s^2*A[1]-320*s^2*A[2]-160*s^2*B[1]-160*s^2*B[2]), 0 = k^3*(beta*s-w)*(A[0]-A[1]+A[2]-B[1]-B[2])*(-5*beta*s*A[0]^2*c[2]+10*beta*s*A[0]*A[1]*c[2]-10*beta*s*A[0]*A[2]*c[2]+10*beta*s*A[0]*B[1]*c[2]+10*beta*s*A[0]*B[2]*c[2]-5*beta*s*A[1]^2*c[2]+10*beta*s*A[1]*A[2]*c[2]-10*beta*s*A[1]*B[1]*c[2]-10*beta*s*A[1]*B[2]*c[2]-5*beta*s*A[2]^2*c[2]+10*beta*s*A[2]*B[1]*c[2]+10*beta*s*A[2]*B[2]*c[2]-5*beta*s*B[1]^2*c[2]-10*beta*s*B[1]*B[2]*c[2]-5*beta*s*B[2]^2*c[2]+3*beta*k*s*w+5*w*A[0]^2*c[2]-10*w*A[0]*A[1]*c[2]+10*w*A[0]*A[2]*c[2]-10*w*A[0]*B[1]*c[2]-10*w*A[0]*B[2]*c[2]+5*w*A[1]^2*c[2]-10*w*A[1]*A[2]*c[2]+10*w*A[1]*B[1]*c[2]+10*w*A[1]*B[2]*c[2]+5*w*A[2]^2*c[2]-10*w*A[2]*B[1]*c[2]-10*w*A[2]*B[2]*c[2]+5*w*B[1]^2*c[2]+10*w*B[1]*B[2]*c[2]+5*w*B[2]^2*c[2]+2*k*s^2-5*k*w^2)]

indets(CoefficientNullity)

{beta, k, s, w, A[0], A[1], A[2], B[1], B[2], c[2]}

(2)

sols := solve(CoefficientNullity, [beta, k, s, w, A[0], A[1], A[2], B[1], B[2], c[2]]); sols := `assuming`([eval(sols)], [b > 0]); whattype(sols); print(cat(`$`('_', 120))); `~`[print](sols)

[[beta = beta, k = 0, s = 0, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]], [beta = beta, k = 0, s = s, w = w, A[0] = A[0], A[1] = 0, A[2] = 0, B[1] = -B[2], B[2] = B[2], c[2] = c[2]], [beta = w/s, k = 0, s = s, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]], [beta = beta, k = 0, s = beta*w, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]]

 

list

 

________________________________________________________________________________________________________________________

 

[beta = beta, k = 0, s = 0, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

 

[beta = beta, k = 0, s = s, w = w, A[0] = A[0], A[1] = 0, A[2] = 0, B[1] = -B[2], B[2] = B[2], c[2] = c[2]]

 

[beta = w/s, k = 0, s = s, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

 

[beta = beta, k = 0, s = beta*w, w = w, A[0] = A[0], A[1] = A[1], A[2] = A[2], B[1] = B[1], B[2] = B[2], c[2] = c[2]]

(3)

Download params.mw

is it possible to ask Maple to verify ode solution obtained from book, which is given in parametric form to check if it is correct?

I know odetest supports both explicit and implicit solutions. But parametric solution is neither of these.

The solution in parametric form makes it look simple to look at and understand, but at same time, not practical in terms of obtaining an explicit solution to verify it and to use it.

The book "handbook of exact solution for ordinary differential equations" by Polyanin and Zaitsev have many such solutions.

Here is one such example of many

I can not just give odetest the y(x) solution above, because the right side depends on tau, which is parameter. If I try to solve for tau in terms of x from the first equation it will become so complicated and odetest hangs. So a whole new different approach is needed as brute force method is not practical in most cases.

restart;

ode:=y(x)*diff(y(x),x)-y(x)=A*x+B;
book_sol:=y(x)=_C1*t*exp( - Int( t/(t^2-t-A),t));
eq:=x=_C1*exp(  - Int( t/(t^2-t-A),t))-B/A;

y(x)*(diff(y(x), x))-y(x) = A*x+B

y(x) = _C1*t*exp(-(Int(t/(t^2-A-t), t)))

x = _C1*exp(-(Int(t/(t^2-A-t), t)))-B/A

value(eq):
solve(%,t):
simplify(eval(book_sol,t=%));

y(x) = _C1*exp(-RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z))+Intat(_a/(-_a^2+A+_a), _a = RootOf(-A*exp(2*RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))+_Z^2-exp(RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))*_Z+1)*exp(-RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))))*RootOf(-A*exp(2*RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))+_Z^2-exp(RootOf(4*A*exp(2*_Z)-4*cosh((ln((A*x+B)/(A*_C1))-_Z)*(4*A+1)^(1/2))^2+exp(2*_Z)))*_Z+1)

odetest(%,ode); #hangs

Download how_to_verify_parametric_solution_to_ode.mw

Some more examples from the book where solutions are given only in parametrric form

update

inspired by solution below by @acer, I found if I just use Solve on the x equation, in order to find t as function of x, and use that in the y equation, it will automatically return solution using RootOf.

Hence no need to explicitly evaluate the integral or explicity set up the RootOf manually.

Now odetest work. 

restart;

ode:=y(x)*diff(y(x),x)-y(x)=A*x+B;
book_sol:=y(x)=_C1*t*exp( - Int( t/(t^2-t-A),t));
eq:=x=_C1*exp(  - Int( t/(t^2-t-A),t))-B/A;

y(x)*(diff(y(x), x))-y(x) = A*x+B

y(x) = _C1*t*exp(-(Int(t/(t^2-A-t), t)))

x = _C1*exp(-(Int(t/(t^2-A-t), t)))-B/A

PDEtools:-Solve(eq,t);

t = RootOf(c__1*exp(Intat(_a/(-_a^2+A+_a), _a = _Z))*A-A*x-B)

simplify(eval(book_sol,%));

y(x) = RootOf(c__1*exp(Intat(_a/(-_a^2+A+_a), _a = _Z))*A-A*x-B)*(A*x+B)/A

odetest(%,ode);

0

#compare to Maple's
simplify(dsolve(ode,useInt));

y(x) = -RootOf(-Intat(_a/(-_a^2+A-_a), _a = _Z)+Intat(1/_a, _a = A*x+B)+c__1)*(A*x+B)/A

odetest(%,ode);

0

 

 

Download how_to_verify_parametric_solution_to_ode_V2.mw

i seperate my equation of real part and imaginary part i want  after taking integrale from my real part we see the pattern betwen real and imaginary part  which they equal about variable beside coefficient , i want to determine and find parameter from real part of my equation then substitute in imaginary for solving but  the number of condition i don't know is how much and there is a little bit repeatation how i can determine the correct one and then substitute ?

restart

with(PDEtools)

undeclare(prime, quiet)

declare(u(x, t), quiet); declare(U(xi), quiet); declare(V(xi), quiet)

pde := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

(1)

G1 := U(-t*v+x) = U(xi); G2 := (D(U))(-t*v+x) = diff(U(xi), xi); G3 := ((D@@2)(U))(-t*v+x) = diff(U(xi), `$`(xi, 2)); G4 := ((D@@3)(U))(-t*v+x) = diff(U(xi), `$`(xi, 3)); G5 := ((D@@4)(U))(-t*v+x) = diff(U(xi), `$`(xi, 4)); G6 := ((D@@5)(U))(-t*v+x) = diff(U(xi), `$`(xi, 5))

T := xi = -t*v+x; T1 := u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

xi = -t*v+x

 

u(x, t) = U(-t*v+x)*exp(I*k*(t*w+x))

(2)

P1 := I*(diff(u(x, t), `$`(t, 2))-s^2*(diff(u(x, t), `$`(x, 2))))+(1/24)*c[1]*(diff(u(x, t), t, `$`(x, 4)))-alpha*s*c[1]*(diff(u(x, t), `$`(x, 5)))+diff(c[2]*u(x, t)*U(-t*v+x)^2, t)-beta*s*(diff(c[2]*u(x, t)*U(-t*v+x)^2, x))

I*(diff(diff(u(x, t), t), t)-s^2*(diff(diff(u(x, t), x), x)))+(1/24)*c[1]*(diff(diff(diff(diff(diff(u(x, t), t), x), x), x), x))-alpha*s*c[1]*(diff(diff(diff(diff(diff(u(x, t), x), x), x), x), x))+c[2]*(diff(u(x, t), t))*U(-t*v+x)^2-2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x)*v-beta*s*(c[2]*(diff(u(x, t), x))*U(-t*v+x)^2+2*c[2]*u(x, t)*U(-t*v+x)*(D(U))(-t*v+x))

(3)

P11 := eval(P1, {T, T1})

I*(((D@@2)(U))(-t*v+x)*v^2*exp(I*k*(t*w+x))-(2*I)*(D(U))(-t*v+x)*v*k*w*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*w^2*exp(I*k*(t*w+x))-s^2*(((D@@2)(U))(-t*v+x)*exp(I*k*(t*w+x))+(2*I)*(D(U))(-t*v+x)*k*exp(I*k*(t*w+x))-U(-t*v+x)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-((D@@5)(U))(-t*v+x)*v*exp(I*k*(t*w+x))+(4*I)*((D@@2)(U))(-t*v+x)*v*k^3*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*w*exp(I*k*(t*w+x))+6*((D@@3)(U))(-t*v+x)*v*k^2*exp(I*k*(t*w+x))-(4*I)*((D@@4)(U))(-t*v+x)*v*k*exp(I*k*(t*w+x))-(6*I)*((D@@2)(U))(-t*v+x)*k^3*w*exp(I*k*(t*w+x))-(D(U))(-t*v+x)*v*k^4*exp(I*k*(t*w+x))+I*((D@@4)(U))(-t*v+x)*k*w*exp(I*k*(t*w+x))-4*((D@@3)(U))(-t*v+x)*k^2*w*exp(I*k*(t*w+x))+4*(D(U))(-t*v+x)*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*(((D@@5)(U))(-t*v+x)*exp(I*k*(t*w+x))+(5*I)*((D@@4)(U))(-t*v+x)*k*exp(I*k*(t*w+x))-10*((D@@3)(U))(-t*v+x)*k^2*exp(I*k*(t*w+x))-(10*I)*((D@@2)(U))(-t*v+x)*k^3*exp(I*k*(t*w+x))+5*(D(U))(-t*v+x)*k^4*exp(I*k*(t*w+x))+I*U(-t*v+x)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(D(U))(-t*v+x)*v*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*w*exp(I*k*(t*w+x)))*U(-t*v+x)^2-2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x)*v-beta*s*(c[2]*((D(U))(-t*v+x)*exp(I*k*(t*w+x))+I*U(-t*v+x)*k*exp(I*k*(t*w+x)))*U(-t*v+x)^2+2*c[2]*U(-t*v+x)^2*exp(I*k*(t*w+x))*(D(U))(-t*v+x))

(4)

P111 := subs({G1, G2, G3, G4, G5, G6}, P11)

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi)))

(5)

pde1 := P111 = 0

I*((diff(diff(U(xi), xi), xi))*v^2*exp(I*k*(t*w+x))-(2*I)*(diff(U(xi), xi))*v*k*w*exp(I*k*(t*w+x))-U(xi)*k^2*w^2*exp(I*k*(t*w+x))-s^2*((diff(diff(U(xi), xi), xi))*exp(I*k*(t*w+x))+(2*I)*(diff(U(xi), xi))*k*exp(I*k*(t*w+x))-U(xi)*k^2*exp(I*k*(t*w+x))))+(1/24)*c[1]*(-(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*exp(I*k*(t*w+x))+(4*I)*(diff(diff(U(xi), xi), xi))*v*k^3*exp(I*k*(t*w+x))+I*U(xi)*k^5*w*exp(I*k*(t*w+x))+6*(diff(diff(diff(U(xi), xi), xi), xi))*v*k^2*exp(I*k*(t*w+x))-(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*k*exp(I*k*(t*w+x))-(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*exp(I*k*(t*w+x))-(diff(U(xi), xi))*v*k^4*exp(I*k*(t*w+x))+I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*exp(I*k*(t*w+x))-4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*exp(I*k*(t*w+x))+4*(diff(U(xi), xi))*k^4*w*exp(I*k*(t*w+x)))-alpha*s*c[1]*((diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*exp(I*k*(t*w+x))+(5*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*exp(I*k*(t*w+x))-10*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*exp(I*k*(t*w+x))-(10*I)*(diff(diff(U(xi), xi), xi))*k^3*exp(I*k*(t*w+x))+5*(diff(U(xi), xi))*k^4*exp(I*k*(t*w+x))+I*U(xi)*k^5*exp(I*k*(t*w+x)))+c[2]*(-(diff(U(xi), xi))*v*exp(I*k*(t*w+x))+I*U(xi)*k*w*exp(I*k*(t*w+x)))*U(xi)^2-2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))*v-beta*s*(c[2]*((diff(U(xi), xi))*exp(I*k*(t*w+x))+I*U(xi)*k*exp(I*k*(t*w+x)))*U(xi)^2+2*c[2]*U(xi)^2*exp(I*k*(t*w+x))*(diff(U(xi), xi))) = 0

(6)

numer(lhs(pde1))*denom(rhs(pde1)) = numer(rhs(pde1))*denom(lhs(pde1))

-exp(I*k*(t*w+x))*((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2) = 0

(7)

%/(-exp(I*k*(t*w+x)))

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]-(24*I)*U(xi)*k^2*s^2+(24*I)*U(xi)*k^2*w^2+(24*I)*U(xi)*alpha*k^5*s*c[1]-(240*I)*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+(24*I)*U(xi)^3*beta*k*s*c[2]+(120*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-I*U(xi)*k^5*w*c[1]-(4*I)*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+(6*I)*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-(24*I)*U(xi)^3*k*w*c[2]+(4*I)*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-I*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1]+(24*I)*(diff(diff(U(xi), xi), xi))*s^2-(24*I)*(diff(diff(U(xi), xi), xi))*v^2 = 0

(8)

Re(%)

Re((diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1])-Im(-24*U(xi)*k^2*s^2+24*U(xi)*k^2*w^2+24*U(xi)*alpha*k^5*s*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]+24*U(xi)^3*beta*k*s*c[2]+120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]-U(xi)*k^5*w*c[1]-4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]+6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]-24*U(xi)^3*k*w*c[2]+4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]-(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]+24*(diff(diff(U(xi), xi), xi))*s^2-24*(diff(diff(U(xi), xi), xi))*v^2) = 0

(9)

R := (diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(diff(U(xi), xi))*k^4*v*c[1]-4*(diff(U(xi), xi))*k^4*w*c[1]-48*(diff(U(xi), xi))*k*v*w+72*c[2]*U(xi)^2*(diff(U(xi), xi))*v-6*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(diff(U(xi), xi), xi), xi))*k^2*w*c[1]+24*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*alpha*s*c[1]+120*(diff(U(xi), xi))*alpha*k^4*s*c[1]+72*(diff(U(xi), xi))*U(xi)^2*beta*s*c[2]-240*(diff(diff(diff(U(xi), xi), xi), xi))*alpha*k^2*s*c[1]-48*(diff(U(xi), xi))*k*s^2+(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi))*v*c[1] = 0

(10)

collect(R, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0

(11)

map(int, (72*beta*s*c[2]+72*v*c[2])*(diff(U(xi), xi))*U(xi)^2+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*(diff(U(xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(diff(U(xi), xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)) = 0, xi)

(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0

(12)

numer(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0)) = numer(rhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))*denom(lhs((24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(1/3)*(72*beta*s*c[2]+72*v*c[2])*U(xi)^3 = 0))

120*U(xi)*alpha*k^4*s*c[1]+U(xi)*k^4*v*c[1]-4*U(xi)*k^4*w*c[1]-240*(diff(diff(U(xi), xi), xi))*alpha*k^2*s*c[1]+24*U(xi)^3*beta*s*c[2]-6*(diff(diff(U(xi), xi), xi))*k^2*v*c[1]+4*(diff(diff(U(xi), xi), xi))*k^2*w*c[1]+24*U(xi)^3*v*c[2]+24*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*s*c[1]-48*U(xi)*k*s^2-48*U(xi)*k*v*w+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*v*c[1] = 0

(13)

RR := collect(%, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

(24*beta*s*c[2]+24*v*c[2])*U(xi)^3+(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w)*U(xi)+(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1])*(diff(diff(U(xi), xi), xi))+(24*alpha*s*c[1]+v*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(14)

IM := 24*U(xi)*k^2*s^2-24*U(xi)*k^2*w^2-24*U(xi)*alpha*k^5*s*c[1]+240*(diff(diff(U(xi), xi), xi))*alpha*k^3*s*c[1]-24*U(xi)^3*beta*k*s*c[2]-120*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*alpha*k*s*c[1]+U(xi)*k^5*w*c[1]+4*(diff(diff(U(xi), xi), xi))*k^3*v*c[1]-6*(diff(diff(U(xi), xi), xi))*k^3*w*c[1]+24*U(xi)^3*k*w*c[2]-4*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*v*c[1]+(diff(diff(diff(diff(U(xi), xi), xi), xi), xi))*k*w*c[1]-24*(diff(diff(U(xi), xi), xi))*s^2+24*(diff(diff(U(xi), xi), xi))*v^2 = 0

collect(IM, {U(xi), diff(U(xi), xi), diff(U(xi), `$`(xi, 3)), diff(diff(U(xi), xi), xi), diff(diff(diff(diff(U(xi), xi), xi), xi), xi), diff(diff(diff(diff(diff(U(xi), xi), xi), xi), xi), xi)})

P := %

(-24*beta*k*s*c[2]+24*k*w*c[2])*U(xi)^3+(-24*alpha*k^5*s*c[1]+k^5*w*c[1]+24*k^2*s^2-24*k^2*w^2)*U(xi)+(240*alpha*k^3*s*c[1]+4*k^3*v*c[1]-6*k^3*w*c[1]-24*s^2+24*v^2)*(diff(diff(U(xi), xi), xi))+(-120*alpha*k*s*c[1]-4*k*v*c[1]+k*w*c[1])*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(15)

NULL

NULL

C1 := v = solve(24*beta*s*c[2]+24*v*c[2] = 0, v)

v = -beta*s

(16)

C2 := w = solve(120*alpha*k^4*s*c[1]+k^4*v*c[1]-4*k^4*w*c[1]-48*k*s^2-48*k*v*w = 0, w)

w = (1/4)*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)/(k^3*c[1]+12*v)

(17)

C3 := alpha = solve(-240*alpha*k^2*s*c[1]-6*k^2*v*c[1]+4*k^2*w*c[1] = 0, alpha)

alpha = -(1/120)*(3*v-2*w)/s

(18)

ode1 := subs({C1, C2, C3}, P)

(-24*beta*k*s*c[2]+6*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[2]/(k^3*c[1]+12*v))*U(xi)^3+((1/5)*(3*v-2*w)*k^5*c[1]+(1/4)*k^5*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)+24*k^2*s^2-(3/2)*k^2*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)^2/(k^3*c[1]+12*v)^2)*U(xi)+(-2*(3*v-2*w)*k^3*c[1]-4*k^3*beta*s*c[1]-(3/2)*k^3*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v)-24*s^2+24*beta^2*s^2)*(diff(diff(U(xi), xi), xi))+((3*v-2*w)*k*c[1]+4*k*beta*s*c[1]+(1/4)*k*(120*alpha*k^3*s*c[1]+k^3*v*c[1]-48*s^2)*c[1]/(k^3*c[1]+12*v))*(diff(diff(diff(diff(U(xi), xi), xi), xi), xi)) = 0

(19)

Download F-condition_and_replacing.mw

I am not sure how to use dsolve for my problem.
CQ_v1.mw

Hi everyone, I am trying to plot graphs for dp/dx versus x from my ordinary differential equation numerically. My file is working, but the outcome is straight lines, which means I am doing something wrong. Could anyone  please have a look on my file.

Help-dpdx.mw

the expected  results should be  look like this

Is there a trick to make Maple simplify 

to

I can't use the exp() trick given in earlier questions, since there is no exp here. Below are my attempts. Can someone find another smart trick to do this simplification? Should simplify() have simplified it as is with no assumptions or using tricks? This is all done in code, so solutions can not depend on "looking on screen" and deciding what to do for each step.

interface(version);

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

restart;

interface(rtablesize=30);

[10, 10]

A:=-(sqrt(3)*sqrt(-2*C1 - 2*x) - 3)/(3*sqrt(-2*C1 - 2*x)*x);

-(1/3)*(3^(1/2)*(-2*C1-2*x)^(1/2)-3)/((-2*C1-2*x)^(1/2)*x)

B:=-(1/(sqrt(3)*x)) + 1/(sqrt(2)*x*sqrt(-x - C1));

-(1/3)*3^(1/2)/x+(1/2)*2^(1/2)/(x*(-x-C1)^(1/2))

simplify(A-B);

0

MmaTranslator:-Mma:-LeafCount(A);
MmaTranslator:-Mma:-LeafCount(B);

29

26

full_simplify:=proc(e::anything,assum::anything)
   local result::list;

   #add more methods as needed

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

end proc:

Vector(full_simplify(A,real))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (6) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (8) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(sqrt(-6*C1-6*x)-3)/((C1+x)*x), (10) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(sqrt(-6*C1-6*x)-3)/(sqrt(-2*C1-2*x)*x)})

Vector(full_simplify(A,positive))

Vector(19, {(1) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (2) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (3) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (4) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (5) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (6) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x), (7) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (8) = -(1/6)*sqrt(2*C1+2*x)*(sqrt(3)*sqrt(2*C1+2*x)+3*I)/((C1+x)*x), (9) = (1/6)*sqrt(-2*C1-2*x)*(I*sqrt(6*C1+6*x)-3)/((C1+x)*x), (10) = (1/3)*(-sqrt(3)*sqrt(2*C1+2*x)-3*I)/(sqrt(2*C1+2*x)*x), (11) = -(1/6)*(2*sqrt(3)*C1+2*sqrt(3)*x+3*sqrt(-2*C1-2*x))/((C1+x)*x), (12) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (13) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (14) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (15) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (16) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (17) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (18) = -(1/3)*(sqrt(3)*sqrt(-2*C1-2*x)-3)/(sqrt(-2*C1-2*x)*x), (19) = -(1/3)*(I*sqrt(6*C1+6*x)-3)/(sqrt(-2*C1-2*x)*x)})

 

 

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