nm - Questions - MaplePrimes

is there difference between running code...

Asked: nm 11523 Product: Maple 2025

October 28 2025

0 1

I am able to reproduce a case where same exact code, which is in .mla library, when called from worksheet produces Maple internal errors when calling odetest, which happens at random places

Error, (in depends) too many levels of recursion

Error, (in anonymous procedure called from depends) too many levels of recursion

But when calling same exact proc in the mla from the command line using

/home/me/maple2025/bin/maple  -q BUILD_ALL.mpl

Where BUILD_ALL.mpl has same command used in worksheet, which is say my_command() where my_command() is proc in my .mla library, the code runs with no erros.

Both worksheet and command use the same exact initialization code before running the command, which is read from this file

dsolve(diff(y(x),x$20)=0,arbitraryconstants=traditional):

interface(warnlevel=0):
kernelopts('assertlevel'=2):

kernelopts(numcpus=1);
kernelopts(gcmaxthreads=1);
interface(rtablesize=100);

latex:-Settings(useimaginaryunit=i,
      usecolor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true,
      usetypesettingcurrentsettings=true,
      linelength=1000000
):

plots[setoptions](font=[TIMES,12], labelfont=[TIMES,16]);
plots[setoptions3d](font=[TIMES,12], labelfont=[TIMES,24]);

_EnvUseHeavisideAsUnitStep:=true;
local gamma;

libname := "/home/me/my.mla", libname:

I see from the print messages I have, that both codes run exactly the same steps as ofcourse should be the case as it is the same function. But when running from worksheet, I keep getting these internal Maple errors when calling odetest in the function called after running for sometime. But no errors from command line.

In the worksheet I have it setup so that each worksheet uses its own math engine.

This also happens when starting from clean worksheet with restart.

So there must be something different in running code in .mla from worksheet vs. command to cause this.

Some sort of memory or stack issue or something like this?. But I have no idea what it can be as I expected same code to run the same way.

I am not able to make MWE so far since it uses the whole .mla and code is very large also code uses SQL database. I tried to make small MWE, but the error from worksheet do not show up then. Only when running the whole program it shows up.

But why does odetest behave different when running code from worksheet vs. command line Maple?

This always happens when calling odetest inside timelimit in the function in question. I also use

`assuming/restore_previous_state`;

In all my try/catch calls. I wonder if this has anything to do with this difference in behavior. I will try next to remove all calls to the above and see if this is what causing the problem. But stil the question is, why behaves different when called from worksheet vs. command line?

I am asking general question here: Should there be difference in how proc() in .mla behaves when called from command line vs. worksheet? Any one had similar experience in Maple?

Any ideas or guesses what can cause this, Or anything I can try to help find the cause? I will try them as I gave up figuring this one.

Does Maple math engine internally makes any checks if it called from worksheet vs. command line? Or does the worksheet itself changes some settings that can cause some math engine function such as odetest to behave different? I do not see how this is can be the case.

Any additional information needed, will be happy to provide it,

(#5654 for my reference)

Update

Good news. I am able to make a MWE which reproduces this bug.

It happens when running many many such calls.

Here is the worksheet. It is large, because the Maple bug only happens when running this sequence of calling odetest. And it happens in worksheet. I will now make version for command line which should not give error. But for now, this is the worksheet version. For me, it gives this error each time. But if you do not see the error, try again from the top of the worksheet.

Note. I am adding the same initialization code I used in both worksheet and command line. Which is

kernelopts(numcpus=1);
kernelopts(gcmaxthreads=1);
interface(rtablesize=100);

to the top of the worksheet. But the Maple error shows up with or without using the above 3 lines of code.

>

restart;

>	interface(version);

>	Physics:-Version();

>	SupportTools:-Version();

>

restart;

>	kernelopts(numcpus=1); kernelopts(gcmaxthreads=1); interface(rtablesize=100);

>

verify_it:=proc(sol,ode,func)
  local the_status;
  try
   the_status:=timelimit(30,odetest(sol,ode,func)):
   if the_statu<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer));
   fi;

   if the_status<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer,positive));
   fi;

   if the_status<>0 then
       the_status:= timelimit(30, (odetest(sol,ode,func) assuming positive));
   fi;

   if the_status<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming x<1));
   fi;

   if the_status<>0 then
      timelimit(30, (odetest(sol,ode,func) assuming x>1));
   fi;
  catch:
   NULL;
  end try:
end proc:

>	#RUN THE next one large cell. If you do not get internal error, try again from restart

>

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):

sol:=Intat(1/(6^(1/3)*tau+(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(2/3
))*(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(1/3),tau = x*y(x)) =
6^(1/3)*ln(x^(1/6))+_C2:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
(27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
(27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=-ln(x) = Intat(-(1+I*3^(1/2))*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(1/3)*6^(2/
3)/_a^(1/2)/(I*3^(5/6)*2^(1/3)+2*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(2/3)-6^
(1/3)),_a = x*y(x))+_C5:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
/3)*z)),z = x(y)*y) = 0:
ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
/2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
2/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
/3)*z)),z = x(y)*y) = 0:
ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
/2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
2/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y(x))-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(
1/2)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^
(2/3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6
^(1/3)*z)),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=-ln(x) = Intat(-2/_a^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(1/3)/(-I*3^(5/
6)*2^(1/3)+I*3^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(2/3)-((27*_a-2)^(1/2
)*3^(1/2)-9*_a^(1/2))^(2/3)-6^(1/3))*6^(2/3),_a = x*y(x))+_C9:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

Error, (in anonymous procedure called from depends) too many levels of recursion

>

Download error_in_worksheet_but_not_in_command_line_oct_28_2025.mw

Below is same exact code but run in command line Maple. It produces no error

#run this A.mpl file using
#/home/me/maple2025/bin/maple A.mpl

interface(version);
Physics:-Version();
SupportTools:-Version();

kernelopts(numcpus=1);
kernelopts(gcmaxthreads=1);
interface(rtablesize=100);

verify_it:=proc(sol,ode,func)
  local the_status;
  try
   the_status:=timelimit(30,odetest(sol,ode,func)):
   if the_statu<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer));
   fi;

   if the_status<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer,positive));
   fi;

   if the_status<>0 then
       the_status:= timelimit(30, (odetest(sol,ode,func) assuming positive));
   fi;

   if the_status<>0 then
      the_status:=timelimit(30, (odetest(sol,ode,func) assuming x<1));
   fi;

   if the_status<>0 then
      timelimit(30, (odetest(sol,ode,func) assuming x>1));
   fi;
  catch:
   NULL;
  end try:
end proc:


sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):


sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
),z = x*y(x)) = 0:
ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
*y(x)^3 = 0:
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):


sol:=Intat(1/(6^(1/3)*tau+(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(2/3
))*(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(1/3),tau = x*y(x)) =
6^(1/3)*ln(x^(1/6))+_C2:
ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
*y(x))*x^2)^(1/3)-1/x*y(x):
verify_it(sol,ode,y(x)):


sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
(27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
(27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=-ln(x) = Intat(-(1+I*3^(1/2))*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(1/3)*6^(2/
3)/_a^(1/2)/(I*3^(5/6)*2^(1/3)+2*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(2/3)-6^
(1/3)),_a = x*y(x))+_C5:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
/3)*z)),z = x(y)*y) = 0:
ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
/2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
2/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
/3)*z)),z = x(y)*y) = 0:
ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
/2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
2/3)):
verify_it(sol,ode,y(x)):

sol:=ln(y(x))-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(
1/2)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^
(2/3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6
^(1/3)*z)),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
),z = x*y(x)) = 0:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):


sol:=-ln(x) = Intat(-2/_a^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(1/3)/(-I*3^(5/
6)*2^(1/3)+I*3^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(2/3)-((27*_a-2)^(1/2
)*3^(1/2)-9*_a^(1/2))^(2/3)-6^(1/3))*6^(2/3),_a = x*y(x))+_C9:
ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
)-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
verify_it(sol,ode,y(x)):

print("DONE. Did you see any errors?");

exit();

Here is the result

>/home/me/maple2025/bin/maple A.mpl
    |\^/|     Maple 2025 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2025
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#run this A.mpl file using
#/home/me/maple2025/bin/maple A.mpl


> interface(version);
                               Command-line Interface, Maple 2025.1, X86 64 LINUX, Jun 12 2025, Build ID 1932578

> Physics:-Version();
The "Physics Updates" version in the MapleCloud is 1881 and is the same as the version installed in this computer, created 2025, October 7, \
    16:4 hours Pacific Time.

> SupportTools:-Version();
The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 202\
    5, 10:25 hours Eastern Time.


> kernelopts(numcpus=1);
                                                                       32

> kernelopts(gcmaxthreads=1);
                                                                    numcpus

> interface(rtablesize=100);
                                                                    [10, 10]


> verify_it:=proc(sol,ode,func)
>   local the_status;
>   try
>    the_status:=timelimit(30,odetest(sol,ode,func)):
>    if the_statu<>0 then
>       the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer));
>    fi;

>    if the_status<>0 then
>       the_status:=timelimit(30, (odetest(sol,ode,func) assuming integer,positive));
>    fi;

>    if the_status<>0 then
>        the_status:= timelimit(30, (odetest(sol,ode,func) assuming positive));
>    fi;

>    if the_status<>0 then
>       the_status:=timelimit(30, (odetest(sol,ode,func) assuming x<1));
>    fi;

>    if the_status<>0 then
>       timelimit(30, (odetest(sol,ode,func) assuming x>1));
>    fi;
>   catch:
>    NULL;
>   end try:
> end proc:


> sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
> *3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
> ^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
> verify_it(sol,ode,y(x)):
memory used=35.6MB, alloc=108.3MB, time=0.19
memory used=121.3MB, alloc=116.3MB, time=0.54
memory used=200.1MB, alloc=144.3MB, time=0.87
memory used=321.1MB, alloc=176.3MB, time=1.35
memory used=384.3MB, alloc=176.3MB, time=1.63
memory used=474.4MB, alloc=176.3MB, time=2.00
memory used=624.5MB, alloc=184.3MB, time=2.57
memory used=759.0MB, alloc=184.3MB, time=3.14
memory used=893.1MB, alloc=184.3MB, time=3.72


> sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
> 2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
> -2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
> verify_it(sol,ode,y(x)):
memory used=1035.8MB, alloc=184.3MB, time=4.27
memory used=1169.9MB, alloc=184.3MB, time=4.83
memory used=1302.5MB, alloc=184.3MB, time=5.38
memory used=1423.7MB, alloc=184.3MB, time=5.90
memory used=1552.0MB, alloc=184.3MB, time=6.42
memory used=1667.7MB, alloc=184.3MB, time=6.93
memory used=1795.9MB, alloc=184.3MB, time=7.46
memory used=1921.7MB, alloc=184.3MB, time=7.99
memory used=2035.4MB, alloc=184.3MB, time=8.49

> sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
> 1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
> (I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
> ),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
> verify_it(sol,ode,y(x)):
memory used=2154.0MB, alloc=184.3MB, time=9.00
memory used=2278.5MB, alloc=184.3MB, time=9.53
memory used=2399.9MB, alloc=184.3MB, time=10.04
memory used=2509.9MB, alloc=184.3MB, time=10.52
memory used=2627.5MB, alloc=184.3MB, time=11.02
memory used=2732.8MB, alloc=184.3MB, time=11.48
memory used=2849.4MB, alloc=184.3MB, time=11.97
memory used=2955.4MB, alloc=184.3MB, time=12.45
memory used=3069.4MB, alloc=184.3MB, time=12.93

> sol:=ln(x)-_C1+Intat(1/z/(-1-1/6/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)*(-6*z*(z
> *3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^(2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3
> ^(1/2)+27*z-1))^(1/3)+z))/z),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
memory used=3173.5MB, alloc=216.3MB, time=13.41
> verify_it(sol,ode,y(x)):
memory used=3322.2MB, alloc=216.3MB, time=14.05
memory used=3466.2MB, alloc=216.3MB, time=14.68
memory used=3605.1MB, alloc=216.3MB, time=15.29
memory used=3743.9MB, alloc=216.3MB, time=15.89
memory used=3882.0MB, alloc=216.3MB, time=16.51

> sol:=ln(x)-_C2+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
> 2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
> -2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
> verify_it(sol,ode,y(x)):
memory used=4029.8MB, alloc=216.3MB, time=17.11
memory used=4159.8MB, alloc=216.3MB, time=17.70
memory used=4299.4MB, alloc=216.3MB, time=18.29
memory used=4434.6MB, alloc=216.3MB, time=18.86
memory used=4557.8MB, alloc=216.3MB, time=19.42
memory used=4701.2MB, alloc=248.3MB, time=20.00

> sol:=ln(x)-_C3+Intat(1/z/(-1-1/4/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)*((-I*3^(
> 1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*
> (I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/z
> ),z = x*y(x)) = 0:
> ode:=2*x^3*diff(y(x),x)^3+6*x^2*y(x)*diff(y(x),x)^2-(1-6*x*y(x))*y(x)*diff(y(x),x)+2
> *y(x)^3 = 0:
> verify_it(sol,ode,y(x)):
memory used=4863.9MB, alloc=248.3MB, time=20.70
memory used=5031.5MB, alloc=248.3MB, time=21.41
memory used=5195.2MB, alloc=248.3MB, time=22.11
memory used=5346.8MB, alloc=248.3MB, time=22.76
memory used=5505.1MB, alloc=248.3MB, time=23.42
memory used=5662.7MB, alloc=248.3MB, time=24.09
memory used=5819.2MB, alloc=248.3MB, time=24.76

> sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
> (2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
> 2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
> x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
> *y(x))*x^2)^(1/3)-1/x*y(x):
> verify_it(sol,ode,y(x)):
memory used=5967.8MB, alloc=248.3MB, time=25.44
memory used=6122.7MB, alloc=248.3MB, time=26.17
memory used=6282.9MB, alloc=280.3MB, time=26.88
memory used=6458.2MB, alloc=280.3MB, time=27.67
memory used=6632.0MB, alloc=280.3MB, time=28.47
memory used=6824.1MB, alloc=280.3MB, time=29.31

> sol:=ln(x)-_C1+Intat(1/z/(-1-1/6*(-6*z*(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)+6^
> (2/3)*((z^3*(-3*(27*z^2-2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z))/(z*3^(1/2)*(27*z^
> 2-2*z)^(1/2)-9*z^2)^(1/3)/z),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
> x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
> *y(x))*x^2)^(1/3)-1/x*y(x):
> verify_it(sol,ode,y(x)):
memory used=6997.3MB, alloc=280.3MB, time=30.11
memory used=7185.8MB, alloc=280.3MB, time=30.94
memory used=7352.2MB, alloc=280.3MB, time=31.70
memory used=7511.5MB, alloc=280.3MB, time=32.44
memory used=7691.1MB, alloc=280.3MB, time=33.23


> sol:=Intat(1/(6^(1/3)*tau+(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(2/3
> ))*(-3^(1/2)*(3*3^(1/2)*tau-(tau*(27*tau-2))^(1/2))*tau)^(1/3),tau = x*y(x)) =
> 6^(1/3)*ln(x^(1/6))+_C2:
> ode:=diff(y(x),x) = 1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(
> x))*x^2)^(1/3)+1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9
> *y(x))*x^2)^(1/3)-1/x*y(x):
> verify_it(sol,ode,y(x)):
memory used=7852.5MB, alloc=312.3MB, time=33.99
memory used=8061.4MB, alloc=312.3MB, time=34.94
memory used=8272.3MB, alloc=312.3MB, time=35.84


> sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
> (27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
> *(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=8467.0MB, alloc=312.3MB, time=36.70
memory used=8678.4MB, alloc=312.3MB, time=37.59
memory used=8886.0MB, alloc=344.3MB, time=38.46
memory used=9099.1MB, alloc=344.3MB, time=39.43
memory used=9317.0MB, alloc=344.3MB, time=40.39
memory used=9549.3MB, alloc=344.3MB, time=41.36

> sol:=ln(x)-_C3+Intat(1/z/(-1-1/4*((-I*3^(1/6)*2^(2/3)-1/3*6^(2/3))*(z^3*(-3*3^(1/2)*
> (27*z^2-2*z)^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)-1/3*6^(2/3)-4*(z*3^(1/2)
> *(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)))/(z*3^(1/2)*(27*z^2-2*z)^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=9758.9MB, alloc=344.3MB, time=42.33
memory used=9986.7MB, alloc=344.3MB, time=43.29
memory used=10213.4MB, alloc=376.3MB, time=44.25
memory used=10438.1MB, alloc=376.3MB, time=45.26
memory used=10674.2MB, alloc=376.3MB, time=46.31
memory used=10939.1MB, alloc=376.3MB, time=47.36

> sol:=-ln(x) = Intat(-(1+I*3^(1/2))*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(1/3)*6^(2/
> 3)/_a^(1/2)/(I*3^(5/6)*2^(1/3)+2*(-(27*_a-2)^(1/2)*3^(1/2)+9*_a^(1/2))^(2/3)-6^
> (1/3)),_a = x*y(x))+_C5:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=11157.9MB, alloc=376.3MB, time=48.37
memory used=11397.1MB, alloc=376.3MB, time=49.36
memory used=11635.9MB, alloc=376.3MB, time=50.33
memory used=11843.8MB, alloc=376.3MB, time=51.27
memory used=12045.3MB, alloc=408.3MB, time=52.21
memory used=12325.2MB, alloc=408.3MB, time=53.28
memory used=12596.4MB, alloc=408.3MB, time=54.33

> sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
> )-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
> 3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
> /3)*z)),z = x(y)*y) = 0:
> ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
> /2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 2/3)):
> verify_it(sol,ode,y(x)):

> sol:=ln(y)-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2
> )-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^(2/
> 3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6^(1
> /3)*z)),z = x(y)*y) = 0:
> ode:=diff(x(y),y) = (3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 1/3)*x(y)^2*6^(2/3)*(I*3^(1/2)-1)/(-1/12*6^(2/3)*(I*3^(1/2)-1)*(-I*6^(2/3)*3^(1
> /2)+6^(2/3)+12*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 1/3))*x(y)*y+2*(3^(1/2)*(-3*3^(1/2)*y+(y*(27*x(y)*y-2)/x(y))^(1/2))*y*x(y)^2)^(
> 2/3)):
> verify_it(sol,ode,y(x)):

> sol:=ln(y(x))-_C6+Intat(1/z/(-1-(1-I*3^(1/2))*z*6^(2/3)*(z^2*(((27*z-2)/z)^(1/2)*3^(
> 1/2)-9))^(1/3)/(-2*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(2/3)+z*(3*I*3^(1/6)*2^
> (2/3)-6^(2/3))*(z^2*(((27*z-2)/z)^(1/2)*3^(1/2)-9))^(1/3)+I*3^(5/6)*2^(1/3)*z+6
> ^(1/3)*z)),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)-1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=12834.3MB, alloc=408.3MB, time=55.38
memory used=13093.0MB, alloc=408.3MB, time=56.51
memory used=13325.7MB, alloc=440.3MB, time=57.54
memory used=13576.1MB, alloc=440.3MB, time=58.67
memory used=13834.9MB, alloc=440.3MB, time=59.79
memory used=14096.1MB, alloc=440.3MB, time=60.95

> sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
> 2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
> -2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=14339.1MB, alloc=440.3MB, time=62.07
memory used=14599.6MB, alloc=440.3MB, time=63.21
memory used=14905.7MB, alloc=504.3MB, time=64.42
memory used=15179.6MB, alloc=488.3MB, time=65.73
memory used=15487.1MB, alloc=488.3MB, time=67.03

> sol:=ln(x)-_C7+Intat(1/z/(-1+1/4*((-I*3^(1/6)*2^(2/3)+1/3*6^(2/3))*(z^3*(-3*(27*z^2-\
> 2*z)^(1/2)*3^(1/2)+27*z-1))^(1/3)+z*(I*3^(1/6)*2^(2/3)+1/3*6^(2/3)+4*(z*(27*z^2
> -2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)))/(z*(27*z^2-2*z)^(1/2)*3^(1/2)-9*z^2)^(1/3)/z
> ),z = x*y(x)) = 0:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=15758.8MB, alloc=488.3MB, time=68.34
memory used=16065.9MB, alloc=520.3MB, time=69.68
memory used=16378.3MB, alloc=520.3MB, time=71.08
memory used=16680.5MB, alloc=520.3MB, time=72.47


> sol:=-ln(x) = Intat(-2/_a^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(1/3)/(-I*3^(5/
> 6)*2^(1/3)+I*3^(1/2)*((27*_a-2)^(1/2)*3^(1/2)-9*_a^(1/2))^(2/3)-((27*_a-2)^(1/2
> )*3^(1/2)-9*_a^(1/2))^(2/3)-6^(1/3))*6^(2/3),_a = x*y(x))+_C9:
> ode:=diff(y(x),x) = -1/12/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2)-9*
> y(x))*x^2)^(1/3)-1/12*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*(y(x)*(27*x*y(x)-2)/x)^(1/2
> )-9*y(x))*x^2)^(1/3)-1/x*y(x)+1/2*I*3^(1/2)*(1/6/x^2*6^(1/3)*(y(x)*(3^(1/2)*(y(
> x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)-1/6*y(x)/x*6^(2/3)/(y(x)*(3^(1/2)*
> (y(x)*(27*x*y(x)-2)/x)^(1/2)-9*y(x))*x^2)^(1/3)):
> verify_it(sol,ode,y(x)):
memory used=16982.9MB, alloc=520.3MB, time=73.86
memory used=17292.8MB, alloc=520.3MB, time=75.22
memory used=17593.5MB, alloc=520.3MB, time=76.51
memory used=17860.3MB, alloc=552.3MB, time=77.77
memory used=18212.4MB, alloc=552.3MB, time=79.18
memory used=18534.1MB, alloc=552.3MB, time=80.58

> print("DONE. Did you see any errors?");
                                                        "DONE. Did you see any errors?"


> exit();
                                                                     exit()

> quit
memory used=18554.9MB, alloc=552.3MB, time=80.69

You see, no error.

why dsolve losses one solution when aske...

Asked: nm 11523 Product: Maple 2025

October 22 2025

1 0

Solving an ode, dsolve says it used exact method and gives two solutions as result (correct result).

But when asking dsolve to solve same ode but now specifying that it uses exact method (i.e. same one it used itself before), now it gives one solution only, not two as before.

Why is that? Should not both commands give same result? i.e. two solutions?

>	interface(version);

>	SupportTools:-Version()

>	Physics:-Version()

>

restart;

>	ode:=3y(x)^3x^2+y(x)^4+(3x^3y(x)^2+y(x)^4+4xy(x)^3)*diff(y(x),x) = 0; DEtools:-odeadvisor(ode); infolevel[dsolve]:=5:

>	sol:=dsolve(ode); #gives two solutions

Classification methods on request

Methods to be used are: [exact]

----------------------------

* Tackling ODE using method: exact

--- Trying classification methods ---

trying exact

<- exact successful

>	maple_sol:=dsolve(ode,[exact]); #why y=0 solution do not show here??

Classification methods on request

Methods to be used are: [exact]

----------------------------

* Tackling ODE using method: exact

--- Trying classification methods ---

trying exact

<- exact successful

>	sol:=dsolve(ode); #gives two solutions again

Classification methods on request

Methods to be used are: [exact]

----------------------------

* Tackling ODE using method: exact

--- Trying classification methods ---

trying exact

<- exact successful

Download why_different_solutions_maple_2025_1_oct_22_2025.mw

How to make solve unaffected by remember...

Asked: nm 11523 Product: Maple 2025

October 21 2025

0 0

Just found strange bug in Maple.

If I do solve(eq1...) then solve(eq2,...) then the second solve now gives internal error.

But If I do (from clean start) just solve(eq2,...) then it times out ok, No internal error. So clearly the first call to solve changed something in internal memory/cache to do this.

Is there a way to correctly "clear" solve cache or its memory tables after each call, so that earlier calls to solve do not affect future calls behavior? Was going to add this to my collection of maple bugs post, but thought a new question will be better to make it easier to reply.

The problem is that these internal Maple errors can not be cought by try/catch. Which means the whole program crashes and there is no way to continue automatically.

>

restart;

>	interface(version);

>	Physics:-Version();

>	SupportTools:-Version();

solve timesout OK if no call made before it

>

restart;

>	kernelopts('assertlevel'=2):

>

eq_2:=1 = -X*((1/2/(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y*(2*Y
*a+2*a*y0)+1/2/(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0*(
2*Y*a+2*a*y0))/(-2*X*Y*a-2*X*a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)-(-a*Y
-a*y0+(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y+(2*X*Y*a+2*
X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0)/(-2*X*Y*a-2*X*a*y0-2*Y*a*
x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)^2*(-2*Y*a-2*a*y0))/Y/((-a+1/2/(2*X*Y*a+2*X*a*
y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y*(2*X*a+2*a*x0-2*Y-2*y0)+(2*X*Y*a
+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)+1/2/(2*X*Y*a+2*X*a*y0+2*Y*a
*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0*(2*X*a+2*a*x0-2*Y-2*y0))/(-2*X*Y*a-2*X*
a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)-(-a*Y-a*y0+(2*X*Y*a+2*X*a*y0+2*Y*a
*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y+(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2
-2*Y*y0-y0^2)^(1/2)*y0)/(-2*X*Y*a-2*X*a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0
^2)^2*(-2*X*a-2*a*x0+2*Y+2*y0)):
try
timelimit(30,solve(identity(eq_2,X),[x0,y0]));
catch:
print("good. No crash");
end try;

Same solve gives internal error when calling another solve before it

>

restart;

>	kernelopts('assertlevel'=2):

>

eq_1:=1 = -X*(1/2*(2*X*Y^3-4*X*Y^2*a+6*X*Y^2*y0-8*X*Y*a*y0+6*X*Y*y0^2-4*X*a*y0^2+2*X*
y0^3+2*Y^3*x0-4*Y^2*a*x0+6*Y^2*x0*y0-8*Y*a*x0*y0+6*Y*x0*y0^2-4*a*x0*y0^2+2*x0*
y0^3+2*X*Y+2*X*y0+2*Y*x0+2*x0*y0)/(X^2*Y*a+X^2*a*y0+2*X*Y*a*x0+2*X*a*x0*y0+Y*a*
x0^2+a*x0^2*y0+X^3+3*X^2*x0+3*X*x0^2+x0^3)-1/2*(X^2*Y^3-2*X^2*Y^2*a+3*X^2*Y^2*
y0-4*X^2*Y*a*y0+3*X^2*Y*y0^2-2*X^2*a*y0^2+X^2*y0^3+2*X*Y^3*x0-4*X*Y^2*a*x0+6*X*
Y^2*x0*y0-8*X*Y*a*x0*y0+6*X*Y*x0*y0^2-4*X*a*x0*y0^2+2*X*x0*y0^3-Y^3*a^2+Y^3*x0^
2-3*Y^2*a^2*y0-2*Y^2*a*x0^2+3*Y^2*x0^2*y0-3*Y*a^2*y0^2-4*Y*a*x0^2*y0+3*Y*x0^2*
y0^2-a^2*y0^3-2*a*x0^2*y0^2+x0^2*y0^3+X^2*Y+X^2*y0+2*X*Y*x0+2*X*x0*y0+Y*x0^2+x0
^2*y0)/(X^2*Y*a+X^2*a*y0+2*X*Y*a*x0+2*X*a*x0*y0+Y*a*x0^2+a*x0^2*y0+X^3+3*X^2*x0
+3*X*x0^2+x0^3)^2*(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0+3*X^2+6*X*x0+3*x0^2))/Y/
(1/2*(3*X^2*Y^2-4*X^2*Y*a+6*X^2*Y*y0-4*X^2*a*y0+3*X^2*y0^2+6*X*Y^2*x0-8*X*Y*a*
x0+12*X*Y*x0*y0-8*X*a*x0*y0+6*X*x0*y0^2-3*Y^2*a^2+3*Y^2*x0^2-6*Y*a^2*y0-4*Y*a*
x0^2+6*Y*x0^2*y0-3*a^2*y0^2-4*a*x0^2*y0+3*x0^2*y0^2+X^2+2*X*x0+x0^2)/(X^2*Y*a+X
^2*a*y0+2*X*Y*a*x0+2*X*a*x0*y0+Y*a*x0^2+a*x0^2*y0+X^3+3*X^2*x0+3*X*x0^2+x0^3)-1
/2*(X^2*Y^3-2*X^2*Y^2*a+3*X^2*Y^2*y0-4*X^2*Y*a*y0+3*X^2*Y*y0^2-2*X^2*a*y0^2+X^2
*y0^3+2*X*Y^3*x0-4*X*Y^2*a*x0+6*X*Y^2*x0*y0-8*X*Y*a*x0*y0+6*X*Y*x0*y0^2-4*X*a*
x0*y0^2+2*X*x0*y0^3-Y^3*a^2+Y^3*x0^2-3*Y^2*a^2*y0-2*Y^2*a*x0^2+3*Y^2*x0^2*y0-3*
Y*a^2*y0^2-4*Y*a*x0^2*y0+3*Y*x0^2*y0^2-a^2*y0^3-2*a*x0^2*y0^2+x0^2*y0^3+X^2*Y+X
^2*y0+2*X*Y*x0+2*X*x0*y0+Y*x0^2+x0^2*y0)/(X^2*Y*a+X^2*a*y0+2*X*Y*a*x0+2*X*a*x0*
y0+Y*a*x0^2+a*x0^2*y0+X^3+3*X^2*x0+3*X*x0^2+x0^3)^2*(X^2*a+2*X*a*x0+a*x0^2)):
timelimit(30,solve(identity(eq_1,X),[x0,y0]));

>	#now try same solve as in first example

>

eq_2:=1 = -X*((1/2/(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y*(2*Y
*a+2*a*y0)+1/2/(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0*(
2*Y*a+2*a*y0))/(-2*X*Y*a-2*X*a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)-(-a*Y
-a*y0+(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y+(2*X*Y*a+2*
X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0)/(-2*X*Y*a-2*X*a*y0-2*Y*a*
x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)^2*(-2*Y*a-2*a*y0))/Y/((-a+1/2/(2*X*Y*a+2*X*a*
y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y*(2*X*a+2*a*x0-2*Y-2*y0)+(2*X*Y*a
+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)+1/2/(2*X*Y*a+2*X*a*y0+2*Y*a
*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*y0*(2*X*a+2*a*x0-2*Y-2*y0))/(-2*X*Y*a-2*X*
a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0^2)-(-a*Y-a*y0+(2*X*Y*a+2*X*a*y0+2*Y*a
*x0+2*a*x0*y0-Y^2-2*Y*y0-y0^2)^(1/2)*Y+(2*X*Y*a+2*X*a*y0+2*Y*a*x0+2*a*x0*y0-Y^2
-2*Y*y0-y0^2)^(1/2)*y0)/(-2*X*Y*a-2*X*a*y0-2*Y*a*x0-2*a*x0*y0+Y^2+2*Y*y0+a^2+y0
^2)^2*(-2*X*a-2*a*x0+2*Y+2*y0)):
try
timelimit(30,solve(identity(eq_2,X),[x0,y0]));
catch:
print("good. No crash");
end try;

Error, (in is/duplicates:-Normal) too many levels of recursion

Download second_sovle_fail_maple_2025_1_oct_21_2025.mw

internal error from odetest, with _EnvAl...

Asked: nm 11523 Product: Maple 2025

October 21 2025

1 0

When solution was obtained using earlier call to solve with _EnvAllSolutions := true: set, then odetest givens internal error.

When _EnvAllSolutions := false: then no error.

Why? And is there a workaround so I can use _EnvAllSolutions := true: but have odetest still work?

>	interface(version);

>	Physics:-Version();

>	SupportTools:-Version();

>

Example fail when using _EnvAllSolutions := true:

>

restart;

>	kernelopts('assertlevel'=2):

>

ode:=diff(y(x),x) = ln(1+y(x)^2);
IC:=y(0)=0;
x0:=0;
sol:=y(x) = -sqrt(-1 + exp(RootOf(-Intat(-1/(2*tau*sqrt(-1 + exp(tau))*exp(-tau)), tau = _Z) + x + _C2)));

eq:=0=eval(rhs(sol),x=x0);
_EnvAllSolutions := true:
_EnvExplicit := true:
sol_C:=_C2=solve(eq,_C2);
sol:=eval(sol,sol_C);
odetest(%,[ode,IC])

y(x) = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+x+_C2)))^(1/2)

0 = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+_C2)))^(1/2)

_C2 = Intat(-(1/2)*exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = (2*I)*Pi*_Z1)

y(x) = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+x+Intat(-(1/2)*exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = (2*I)*Pi*_Z1))))^(1/2)

Error, (in series/csgn) assertion failed

>

Example Works when using _EnvAllSolutions := false:

>

restart;

>	kernelopts('assertlevel'=2):

>

ode:=diff(y(x),x) = ln(1+y(x)^2);
IC:=y(0)=0;
x0:=0;
sol:=y(x) = -sqrt(-1 + exp(RootOf(-Intat(-1/(2*tau*sqrt(-1 + exp(tau))*exp(-tau)), tau = _Z) + x + _C2)));

eq:=0=eval(rhs(sol),x=x0);
_EnvAllSolutions := false:
_EnvExplicit := true:
sol_C:=_C2=solve(eq,_C2);
sol:=eval(sol,sol_C);
odetest(%,[ode,IC])

y(x) = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+x+_C2)))^(1/2)

0 = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+_C2)))^(1/2)

_C2 = Intat(-(1/2)*exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = 0)

y(x) = -(-1+exp(RootOf(-Intat(-(1/2)/(tau*(-1+exp(tau))^(1/2)*exp(-tau)), tau = _Z)+x+Intat(-(1/2)*exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = 0))))^(1/2)

[RootOf(Intat(exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = _Z)+2*x-Intat(exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = 0))-ln(exp(RootOf(Intat(exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = _Z)+2*x-Intat(exp(tau)/(tau*(-1+exp(tau))^(1/2)), tau = 0)))), 0]

Download odetest_fail_when_using_envAllsol_maple_2025_1_oct_21_2025.mw

are c__1 and _C1 no longer same object i...

Asked: nm 11523 Product: Maple 2025

October 19 2025

2 0

The nice addition added to Maple 2022 in this post made it clear that c__1 and _C1 are the same under the cover.

But then why in Maple 2025.1 it does not give this?

I found this when I was trying to find constants of integrations in solution of an ode, and used

indets(sol,And(symbol, suffixed(_C, nonnegint)));

Which did not find the constants of integration, since I happened to have typed the solution using c__1 and not _C1, but I thought they are the same.

Did something change or I still dont understand well the difference between c__1 and _C1 ?

Worksheet below.

>	interface(version);

>	SupportTools:-Version();

>	Physics:-Version();

>

restart;

>	sol:= y(x)=-cos(x)/2+sin(x)/2+c__1*exp(-x); indets(sol,And(symbol, suffixed(_C, nonnegint)));

>	sol:= y(x)=-cos(x)/2+sin(x)/2+c__1*exp(-x); indets(sol,And(symbol, suffixed(c__, nonnegint)));

${c__1}$

>	sol:= y(x)=-cos(x)/2+sin(x)/2+_C1*exp(-x); indets(sol,And(symbol, suffixed(c__, nonnegint)));

>	sol:= y(x)=-cos(x)/2+sin(x)/2+_C1*exp(-x); indets(sol,And(symbol, suffixed(_C, nonnegint)));

${_C1}$

>	c__1 - _C1

>	addressof(c__1);

>	addressof(_C1);

Download why_c1_and_C1_not_same_oct_19_2025.mw

Update

Found out why. This only works if one calls dsolve() first. Here is an example

Download why_c1_and_C1_not_same_oct_19_2025_V1.mw

But this is really confusing. c__1 before calling dsolve is not the same as c__1 after calling dsolve.

It will be better if Maple is changed such that these work the same all the time without having to call dsolve() first.

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is there difference between running code...

why dsolve losses one solution when aske...

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