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dsolve does not return solution unless g...

nm 9794 Maple 2024
ode dsolve implicit
July 18 2024
1 0

I have thought before that Maple's dsolve will try to return implicit solution automatically if unable to find explicit one or for some  other reasons it prefers implicit.

But In this ode, we see Maple returns no solution at all for this first order quadrature ode, even though it can find solution when given implicit option.

Is this a correct behaviour? Should it not have returned this solution automatically?

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1774 and is the same as the version installed in this computer, created 2024, July 16, 17:18 hours Pacific Time.`

> 

restart;
> 

ode:=diff(y(x),x)=sin(y(x));
IC:=y(a)=b;

diff(y(x), x) = sin(y(x))

y(a) = b

> 

maple_sol:=dsolve([ode,IC]);

> 

maple_sol:=dsolve([ode,IC],explicit);

> 

maple_sol:=dsolve([ode,IC],implicit);

x-ln(csc(y(x))-cot(y(x)))-a+ln(csc(b)-cot(b)) = 0

 

 

Download why_no_solution_by_dsolve_july_18_2024.mw

Update

I found another example of this problem. Maple gives no solution to this ODE unless option implicit is given. This is not right behaviour. If Maple can't give explicit solution, it should return the implicit one automatically. How is the user supposed to know there is a solution to this ode otherwise?
 

> 

restart;
> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1786 and is the same as the version installed in this computer, created 2024, August 10, 8:50 hours Pacific Time.`

> 

restart;
> 

libname;

"C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib", "C:\Program Files\Maple 2024\lib"

> 

ode:=(x^2+y(x)^2-2*y(x))*diff(y(x),x) = 2*x:
IC:=y(0)=1:
sol:=dsolve([ode,IC],y(x));

> 

sol:=dsolve([ode,IC],y(x),'implicit');

-exp(-1)+exp(-y(x))*x^2+exp(-y(x))*y(x)^2 = 0

> 

sol:=dsolve([ode,IC],y(x),'useInt');

y(x) = -RootOf(exp(_Z)*x^2-(Int(_b*(_b-2)/exp(_a), _b = 0 .. -_Z))+Int(_b*(_b-2)/exp(_a), _b = 0 .. 1))

> 

sol:=dsolve([ode,IC],y(x),'explicit');

> 

 


 

Download why_does_not_solve_unless_implicit_august_12_2024.mw

 

Maple 2024.1 locks up completely when us...

nm 9794 Maple 2024
typesetting dsolve gui
July 17 2024
0 6

I called dsolve with timelimit on this ode.  All of Maple instantly locks up.

I do not mean the worksheet, but everything. I have each worksheet using its own engine,. Not able to open new worksheet, nothing clicks. The whole front end locks up. Can't click on anything. 

Killing every mserver.exe does not even resolve this. I had to terminate all of Maple from the task manager. The strange thing, is that looking at task manager I see mserver.exe doing nothing. zero CPU. Only the front end process is at high CPU (the one with the Java icon).  It looks like the Java frontend is locked up for some reason.

 

Do others see the same thing? does this happen on the mac also? Please make sure to save all your work before trying to run this on your PC.

Maple 2024.1 on windows 10. This is first order Riccati ode.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1774 and is the same as the version installed in this computer, created 2024, July 16, 17:18 hours Pacific Time.`

> 

ode:=(a2*x^2+b2*x+c2)*diff(y(x),x)=y(x)^2+(a1*x+b1)*y(x)+a0*x^2+b0*x+c0;

(a2*x^2+b2*x+c2)*(diff(y(x), x)) = y(x)^2+(a1*x+b1)*y(x)+a0*x^2+b0*x+c0

> 

DEtools:-odeadvisor(ode);

[_rational, _Riccati]

> 

#WARNING. This will freeze all of Maple.
timelimit(30,dsolve(ode));


Download maple_lock_up_july_17_2024.mw

These are GUI options on my end.

 

 

 

 

UPDATE 1

in Maple 2023.2 also on windows 10,  there is no lock up at all. same code. The solution to the ode is very large. I tried using both typesetting level  to EXTENDED  and  typesetting level MAPLE STANDARD and no hang.

I wonder if this has something to do with why Maple 2024.1 locks up? But I have not changed anything in my end. I made no change in options or anything else. same PC, same graphics card. 

UPDATE 2

Found the BUG!!  

In Maple 2024.1, if I change the display option typesetting level  to EXTENDED, the front end do not hang.

If I change the display typesetting level MAPLE STANDARD, the ftont end hangs.

But why??


 

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1774 and is the same as the version installed in this computer, created 2024, July 16, 17:18 hours Pacific Time.`

> 

ode:=(a2*x^2+b2*x+c2)*diff(y(x),x)=y(x)^2+(a1*x+b1)*y(x)+a0*x^2+b0*x+c0;

(a2*x^2+b2*x+c2)*(diff(y(x), x)) = y(x)^2+(a1*x+b1)*y(x)+a0*x^2+b0*x+c0

> 

DEtools:-odeadvisor(ode);

[_rational, _Riccati]

> 

interface(typesetting=extended):
> 

timelimit(30,dsolve(ode));

`[Length of output exceeds limit of 1000000]`

> 

interface(typesetting=standard):
> 

#WARNING, this will hang MAPLE now. WHY??
timelimit(30,dsolve(ode));


 

Download maple_lock_up_july_17_2024_2.mw

ps. Reported to Maplesoft support. July 17, 2024. Hopefully this will be fixed in Maple 2024.2

 

c__1 and _C1 do not seem to work the sam...

nm 9794 Maple 2024
constants ode dsolve
July 09 2024
2 2

The change from _C1 to c__1 is causing me so many problems as I still do not fully understand it.

I have nothing in my Maple ini file. 

I was solving from a solution to an ode for the constant of integration, which I know is c__1 inside a proc.

But this was failing to solve for it. When I copy same code to global (worksheet), it works. So it is clearly issue of name space related to c__1 vs. _C1. 

So even though the solution now has the subscripted version and not the traditional one (since that is the default now), it does not solve for it when inside a proc.

If instead I solve for _C1, then it works. Even though the solution has c__1. This is bizzar to me. 

I also tried adding   global c__1; inside the proc, but this did not help. (did not show this version in the worksheet).

Why is solving for c__1 fail inside a proc but works outside? Clearly the c__1 in the solution of the ode is not the same c__1 I typed in to solve for, even though on the screen they look the same. 

So c__1 is not really the same as _C1 in all aspects. Right?

Here is worksheet. Example 1 below shows how it fails inside proc

Maple 2024.1. Does this happen for others on Linux or the Mac?
 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1767 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

Example (1) solving for constant of integration fails inside proc but works outside

 
> 

restart;

> 

foo:=proc(ode::`=`)
local sol,the_constant;
   sol:=dsolve(ode);
   print("sol is ",sol);
   the_constant:=solve(sol,c__1);
   print("the constant is ",the_constant);
end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode); print("sol is ", sol); the_constant := solve(sol, c__1); print("the constant is ", the_constant) end proc

> 

#this does not work
ode:=diff(y(x),x) = 3/4*y(x)/x;
foo(ode)

diff(y(x), x) = (3/4)*y(x)/x

"sol is ", y(x) = c__1*x^(3/4)

"the constant is "

> 

restart;

> 

#this works
ode:=diff(y(x),x) = 3/4*y(x)/x;
sol:=dsolve(ode);
print("sol is ",sol);
the_constant:=solve(sol,c__1);

diff(y(x), x) = (3/4)*y(x)/x

y(x) = c__1*x^(3/4)

"sol is ", y(x) = c__1*x^(3/4)

y(x)/x^(3/4)

> 

 

Example (2). Solving for _C1 works, even though the ode has c__1  , why??

 
> 

restart;

> 

foo:=proc(ode::`=`)
local sol,the_constant;
   sol:=dsolve(ode);
   print("sol is ",sol);
   the_constant:=solve(sol,_C1);  #notice solving for _C1 now
   print("the constant is ",the_constant);
end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode); print("sol is ", sol); the_constant := solve(sol, _C1); print("the constant is ", the_constant) end proc

> 

ode:=diff(y(x),x) = 3/4*y(x)/x;
foo(ode)

diff(y(x), x) = (3/4)*y(x)/x

"sol is ", y(x) = c__1*x^(3/4)

"the constant is ", y(x)/x^(3/4)

> 

restart;

> 

ode:=diff(y(x),x) = 3/4*y(x)/x;
sol:=dsolve(ode);
print("sol is ",sol);
the_constant:=solve(sol,c__1); #these both work OK in global
the_constant:=solve(sol,_C1);  #these both work OK in global

diff(y(x), x) = (3/4)*y(x)/x

y(x) = c__1*x^(3/4)

"sol is ", y(x) = c__1*x^(3/4)

y(x)/x^(3/4)

y(x)/x^(3/4)

> 

 

> 

 

Example (3). Forcing arbitraryconstants = subscripted it still does not work inside proc. Why??

 
> 

restart;

> 

foo:=proc(ode::`=`)
local sol,the_constant;
   sol:=dsolve(ode,arbitraryconstants = subscripted);   
   print("sol is ",sol);
   the_constant:=solve(sol,c__1);
   print("the constant is ",the_constant);
end proc;

proc (ode::`=`) local sol, the_constant; sol := dsolve(ode, arbitraryconstants = subscripted); print("sol is ", sol); the_constant := solve(sol, c__1); print("the constant is ", the_constant) end proc

> 

ode:=diff(y(x),x) = 3/4*y(x)/x;
foo(ode)

diff(y(x), x) = (3/4)*y(x)/x

"sol is ", y(x) = c__1*x^(3/4)

"the constant is "

> 

 


 

Download constant_of_integration_solving_july_9_2024_maple_2024.mw

 

Error, (in RootOf) _Z occurs but is not ...

nm 9794 Maple 2024
rootof radnormal
July 07 2024
0 3

I added radnormal(sol) to my solution to workaround bug in solve hanging. 

But now new problem showed up. sometimes radnormal gives internal error when there are _Z's in solution.

radnormal(sol);
Error, (in RootOf) _Z occurs but is not the dependent variable
 

Attached worksheet. Sorry that the solution is very large and has lots of _Zs and RootOf, but this is the first one I can see so far in the log file of my program running, so I left it as is:

Should I check in my code that solution does not contain _Z before calling radnormal on it?  Is this a bug or known limitation?
 

> 

restart;
> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1767 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

> 

sol:=1/6*(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) + 1/6*(4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2 + 2*a*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2) + a^2)/(-a^3 - 3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 + 6*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a + 8*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 + 3*sqrt(3)*sqrt(-RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*(RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^4 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a^3 + 4*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3*a^2 + 4*a^3 + 12*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)*a^2 - 24*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^2*a - 32*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2)^3 - 108*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))) + 54*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2))^(1/3) - 1/6*a + 1/3*RootOf(4*_Z^2 - 4*_Z*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + 2*a*_Z + (8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(2/3) - a*(8*_Z^3 + 6*_Z^2*a - 3*_Z*a^2 - a^3 + 3*sqrt(3)*sqrt(-4*_Z^4*a^2 - 4*_Z^3*a^3 - _Z^2*a^4 + 32*_Z^4 + 24*_Z^3*a - 12*_Z^2*a^2 - 4*_Z*a^3 + 108*_Z^2) + 54*_Z)^(1/3) + a^2):
> 

radnormal(sol);

Error, (in RootOf) _Z occurs but is not the dependent variable

> 

 


 

Download bug_Z.mw

two solutions, exactly the same, one han...

nm 9794 Maple 2024
ode radical simplification
July 06 2024
1 1

I gave up trying to figure out why Maple sometimes generates solutions from my code that look different, running the same exact code. I know Maple is not deterministic and this can happen sometimes for reasons I will never know.

The following two solutions are the same, it just sometimes Maple shuffles terms a little around. For example SQRT(6) comes out SQRT(2)*SQRT(3).  I have no idea why this happens. It could be how memory inside Maple happened to be at the time and what happened before.

But my question is the following. Here is one ode, and two solutions that are exactly the same. I called one good_sol and one bad_sol.

If I do simplify(bad_sol - good_sol) I get  0 = 0 but here is the problem. When calling odetest on the good_sol, Maple returns 0 instantly,  But on the bad_sol it just hangs.

Even though the two solution are exactly the same. i.e. Mathematically the same.  

I'd like to know why does this happen? And if there is a permanent fix I could always use.

The following worksheet shows this problem.

After much trial and error, I found that if I do radnormal(bad_sol) then now odetest returns zero right away and the hang is gone!

I am just trying to understand why. And why odetest then itself does not use radnormal if this makes it work better?

Do I need to call randormal on every solution before calling odetest then? Will calling randormal on the final solution have any bad side effects on other computation after that?  It should not I would think.

This is all done in code without looking at the screen and having to decide. So I would need a solution that will work for all cases. But for now, I will change my code and add randormal to all solutions and see what happens.

Using 2024.1 on windows.   May be Maple behaves different on macOS, I do not know.

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.1, Windows 10, June 25 2024 Build ID 1835466`

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1767 and is the same as the version installed in this computer, created 2024, June 28, 12:19 hours Pacific Time.`

> 

restart;
> 

ode:=4*x*diff(y(x),x)^2-3*y(x)*diff(y(x),x)+3 = 0;

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

> 

bad_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))/sqrt(x)) + 1/2*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) + 1/2*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(2)*sqrt(3))*sqrt(2)/(sqrt((3*y(x)^2 - 16*x)/x)*sqrt(x))) = 0;

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*2^(1/2)*3^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))) = 0

> 

good_sol:=ln(x) - c__1 - 1/2*ln((y(x)^2 - 6*x)/x) - 3*ln((sqrt(3)*y(x) + sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))/sqrt(x)) + 1/12*sqrt(3)*sqrt(6)*sqrt(2)*arctanh(1/2*(-16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x))) + 1/12*sqrt(3)*arctanh(1/2*(16*sqrt(x) + 3*y(x)*sqrt(6))*sqrt(2)/(sqrt(x)*sqrt((3*y(x)^2 - 16*x)/x)))*sqrt(6)*sqrt(2) = 0;
 

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((3^(1/2)*y(x)+((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2))/x^(1/2))+(1/12)*3^(1/2)*6^(1/2)*2^(1/2)*arctanh((1/2)*(-16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))+(1/12)*3^(1/2)*arctanh((1/2)*(16*x^(1/2)+3*y(x)*6^(1/2))*2^(1/2)/(((3*y(x)^2-16*x)/x)^(1/2)*x^(1/2)))*6^(1/2)*2^(1/2) = 0

> 

simplify(bad_sol-good_sol)

0 = 0

> 

odetest(good_sol,ode); #instant answer

0

> 

odetest(bad_sol,ode); #hangs

Warning,  computation interrupted

> 

 

> 

radnormal(bad_sol)

ln(x)-c__1-(1/2)*ln((y(x)^2-6*x)/x)-3*ln((y(x)*x^(1/2)*3^(1/2)+x*(-(-3*y(x)^2+16*x)/x)^(1/2))/x)+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)-8*2^(1/2)*x)/(3*y(x)^2-16*x))+(1/2)*arctanh((-(-3*y(x)^2+16*x)/x)^(1/2)*(3*y(x)*x^(1/2)*3^(1/2)+8*2^(1/2)*x)/(3*y(x)^2-16*x)) = 0

> 

odetest(%,ode); #instant answer

0

> 

 


 

Download why_same_sol_hangs_july_7_2024.mw

 

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