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Bug report: Error, (in dsolve) invalid s...

Asked: nm 11353 Product: Maple 2024

December 27 2024

0 2

I do not remember if I reported this before or not. Can't find it. Just in case, I am posting this.

If someone find it is duplicate, feel free to delete this. But this is in latest Maple 2024.2. May be this can be fixed in time by Maple 2025 version.

>

restart;

>	interface(version);

>	Physics:-Version();

>

libname;

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

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0;

(diff(y(x), x))/y(x)-(3/2)*(4*x^2+y(x)^2+1)/(x*(4*x^2+y(x)^2-2-2*x)) = 0

>	DEtools:-odeadvisor(ode);

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

>

restart;

>	infolevel[dsolve]:=5;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

trying Bernoulli

trying separable

trying inverse linear

trying homogeneous types:

trying Chini

differential order: 1; looking for linear symmetries

trying exact

Looking for potential symmetries

trying inverse_Riccati

trying an equivalence to an Abel ODE

equivalence obtained to this Abel ODE: diff(y(x),x) = 3/2*(4*x^2+1)/x/(2*x^2-x-1)*y(x)-(x^2+2*x+3)/x/(2*x^2-x-1)^2*y(x)^2+3/8*(2*x+3)/(2*x^2-x-1)^3/x*y(x)^3

trying to solve the Abel ODE ...

The relative invariant s3 is: -1/432*(8*x^4+40*x^3+45*x^2-270*x+135)/x^3/(x-1)^6/(2*x+1)^4

The first absolute invariant s5^3/s3^5 is: 729/16*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^3/(2*x+1)^4/(8*x^4+40*x^3+45*x^2-270*x+135)^5

The second absolute invariant s3*s7/s5^2 is: 1/3*(8*x^4+40*x^3+45*x^2-270*x+135)*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)^2

...checking Abel class AIL (45)

...checking Abel class AIL (310)

...checking Abel class AIR (36)

...checking Abel class AIL (301)

...checking Abel class AIL (1000)

...checking Abel class AIL (42)

...checking Abel class AIL (185)

...checking Abel class AIA (by Halphen)

...checking Abel class AIL (205)

...checking Abel class AIA (147)

...checking Abel class AIL (581)

...checking Abel class AIL (200)

...checking Abel class AIL (257)

...checking Abel class AIL (400)

...checking Abel class AIA (515)

...checking Abel class AIR (1001)

...checking Abel class AIA (201)

...checking Abel class AIA (815)

Looking for potential symmetries

... changing x -> 1/x, trying again

Looking for potential symmetries

The third absolute invariant s5*s7/s3^4 is: 243/16*(10240*x^12+133120*x^11+697600*x^10+1710080*x^9+3358592*x^8-1701568*x^7+6692592*x^6-18182448*x^5+2088072*x^4-7938000*x^3+2525985*x^2+1786050*x+2679075)/(2*x+1)^4*(128*x^8+1152*x^7+3696*x^6+1744*x^5+8148*x^4-31500*x^3+6615*x^2-5670*x+8505)/(8*x^4+40*x^3+45*x^2-270*x+135)^4

-> ======================================

-> ...checking Abel class D (by Appell)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {4/27} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class B (by Liouville)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {1, 4, 1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class A (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -1/4} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class C (by Abel)

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {2, -11676447873119/75975070592769, 9/5, 15632211369872/75439744512117, 46273613050865/52325357771027, 75312059745574/25138886548531} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 9/5 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.6

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-4, 16} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.8

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -116457391291688/45108305127449, -96869842492381/35485755507516, -36964550865207/94238117721032, -32286830321303/11596568583712, 32286830321303/11596568583712, 36964550865207/94238117721032, 96869842492381/35485755507516, 116457391291688/45108305127449} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIL 1.9

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-2/9, -1/9} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.51

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {0, -94917840318055/84247876515289, -85939756880989/51399391393709, -82210125508529/36853933366676, -74381886667083/82545981233858, -41168492684238/33804146399567, -15658703496425/19275443365317, -9175348901453/101481647952193, 3/4, 15/4, 5568553686203/113599855351490, 12774469621703/63437040534358, 17836021821409/102823494563886, 39657708622139/74009717243016, 82495450887526/27663991325651, 86656182727564/45157560524183, 90074893410229/54954593917906, 100200889070747/32282555481919, 113612565327585/103754255779069} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = 15/4 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.5

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-1, 1, -113553630998996/78694251194667, -112790344818825/35834119404842, -104905620984375/18860524785743, -95409943222181/78810323073434, -77648002983645/31218435062578, -67259194033608/9576982470445, -46892223838816/86694928762723, -45901561561111/29768419326991, -34674701564566/6522678435631, 26154715634141/21099761863911, 42841215778132/81925179545457, 52638927823233/15127919203723, 54069389554571/5444364811188, 54445812264368/10328928623117, 56815569067370/40738034746481, 75614540760757/62881656939350, 76459718737483/64786816765621, 85896394925571/88677987470966, 90623073438172/24246571690325, 103628692054633/17857341616628, 117754725919014/60191028908095} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -1 leads to a useless solution (F does not depend on x)

_____________________________

C = -113553630998996/78694251194667 leads to a useless solution (F does not depend on x)

_____________________________

C = -112790344818825/35834119404842 leads to a useless solution (F does not depend on x)

_____________________________

C = -104905620984375/18860524785743 leads to a useless solution (F does not depend on x)

_____________________________

C = -95409943222181/78810323073434 leads to a useless solution (F does not depend on x)

_____________________________

C = -77648002983645/31218435062578 leads to a useless solution (F does not depend on x)

_____________________________

C = -67259194033608/9576982470445 leads to a useless solution (F does not depend on x)

_____________________________

C = -46892223838816/86694928762723 leads to a useless solution (F does not depend on x)

_____________________________

C = -45901561561111/29768419326991 leads to a useless solution (F does not depend on x)

_____________________________

C = -34674701564566/6522678435631 leads to a useless solution (F does not depend on x)

_____________________________

C = 26154715634141/21099761863911 leads to a useless solution (F does not depend on x)

_____________________________

C = 42841215778132/81925179545457 leads to a useless solution (F does not depend on x)

_____________________________

C = 52638927823233/15127919203723 leads to a useless solution (F does not depend on x)

_____________________________

C = 54069389554571/5444364811188 leads to a useless solution (F does not depend on x)

_____________________________

C = 54445812264368/10328928623117 leads to a useless solution (F does not depend on x)

_____________________________

C = 56815569067370/40738034746481 leads to a useless solution (F does not depend on x)

_____________________________

C = 75614540760757/62881656939350 leads to a useless solution (F does not depend on x)

_____________________________

C = 76459718737483/64786816765621 leads to a useless solution (F does not depend on x)

_____________________________

C = 85896394925571/88677987470966 leads to a useless solution (F does not depend on x)

_____________________________

C = 90623073438172/24246571690325 leads to a useless solution (F does not depend on x)

_____________________________

C = 103628692054633/17857341616628 leads to a useless solution (F does not depend on x)

_____________________________

C = 117754725919014/60191028908095 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.52

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-5, -4, -3, 0, 1, 2, -3/2} ***

-> Step 3: looking for a solution F depending on x

*** No solution F of x was found ***

-> ======================================

-> ...checking Abel class AIA 1.53

-> Step 1: checking for a disqualifying factor on F after evaluating x at a number

Trying x = 2

*** No disqualifying factor on F was found ***

-> Step 2: calculating resultants to eliminate F and get candidates for C

*** Candidates for C are {-3, -1, 1, 2, -3/2, -2/3, -1/2} ***

-> Step 3: looking for a solution F depending on x

_____________________________

C = -3 leads to a useless solution (F does not depend on x)

_____________________________

C = -3/2 leads to a useless solution (F does not depend on x)

*** No solution F of x was found ***

trying to map the Abel into a solvable 2nd order ODE

...checking Abel class AIA 2-parameter, reducible to Riccati

Error, (in dsolve) invalid subscript selector

>

restart;

>	ode := diff(y(x),x)/y(x)-(3(4x^2+y(x)^2+1))/(2x(4x^2+y(x)^2-2-2x))=0:

>	dsolve(ode,y(x));

Error, (in dsolve) invalid subscript selector

>	tracelast;

Error, (in dsolve) invalid subscript selector

Download dsolve_invalid_subscript_dec_27_2024.mw

Error, (in dsolve) type `System` does no...

Asked: nm 11353 Product: Maple 2024

December 26 2024

0 4

I am trying to see if I can get speed up by using dsolve inside thread.

I made very simple example of global list of two differential equations to start with.

Next, created two threads where each picks one ode from the global list to process. So they should in theory run in parallel. The list of ode's is a global list in the worksheet for now.

But I keep getting error when calling dsolve

Error, (in dsolve) type `System` does not exist

I tried also passing the actual ode to the thread, still, same error.

Next, I did not pass anything, but called dsolve directly from inside thread proc on same ode. The ode is local variable inside the proc. I still get same error.

Does this mean dsolve is not supported by threads?

But when I searched this subject, AI says it works in threads:

Everything works OK when I run dsolve in worksheet outside thread (i.e. normally).

I will show below worksheet showing these cases. I must not be doing something right. But what? Can one not pass data from global worksheet to the thread this way? Or does one needs to load something in each thread to make this work?

>	interface(version);

>	Physics:-Version();

>

libname;

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

Example 1. Passing index of list to thread

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(i::posint) :-dsolve(g_list[i]): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(i)), i=1..2) );

Error, (in dsolve) type `System` does not exist

Example 2. Passing actual ode itself to thread

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(ode::`=`) :-dsolve(ode): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(g_list[i])), i=1..2) );

Error, (in dsolve) type `System` does not exist

>

Example 3. Normal processing. No threads

>

restart;

>	g_list:=[sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2x(t)=0, diff(y(x),x)=lambdasin(lambdax)y(x)^2+acos(lambdax)^ny(x)-acos(lambda*x)^(n-1)]:

>	work_func:=proc(ode::`=`) :-dsolve(ode): end proc:

>	for item in g_list do work_func(item); od:

>

#no error

>

Example 4. do not pass anything. Just call dsolve

>

restart;

>	work_func:=proc(i::posint) local x,t; local ode:=sin(t)diff(x(t),t$2)+cos(t)diff(x(t),t)+2*x(t)=0; :-dsolve(ode): end proc:

>	Threads:-Wait( seq( Threads:-Create( work_func(i)), i=1..2) );

Error, (in dsolve) type `System` does not exist

>

Download error_dsolve_using_threads_dec_26_2024.mw

Bug report: dsolve generates internal er...

Asked: nm 11353 Product: Maple 2024

December 25 2024

2 3

This is an ode from textbook. dsolve gives new error I have not seen before.

Maple 2024.2 on windows 10.

>	interface(version);

>	Physics:-Version();

>

restart;

>

libname;

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

>	ode:=y(x)^2diff(y(x),x$3)-(3y(x)diff(y(x),x)+2xy(x)^2 )diff(y(x),x$2)+(2diff(y(x),x)^2+2xy(x)diff(y(x),x)+3x^2y(x)^2)diff(y(x),x)+x^3y(x)^3=0;

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

>	dsolve(ode);

Error, (in factor) too many levels of recursion

>	infolevel[dsolve]:=5;

>	dsolve(ode);

Methods for third order ODEs:

--- Trying classification methods ---

trying 3rd order ODE linearizable_by_differentiation

differential order: 3; trying a linearization to 4th order

trying differential order: 3; missing variables

trying differential order: 3; exact nonlinear

trying 3rd order, integrating factor of the form mu(y'') for some mu

Trying the formal computation of integrating factors depending on any 2 of [x, y, y', y'']

*** Sublevel 2 ***

Methods for first order ODEs:

--- Trying classification methods ---

trying a quadrature

trying 1st order linear

<- 1st order linear successful

Successful computation of 3 integrating factors: [x*exp(-1/2*x^2*(I*2^(1/2)+1))*KummerM(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2)/y(x), x*exp(-1/2*x^2*(I*2^(1/2)+1))*KummerU(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2)/y(x), x*exp(-1/2*x^2*(I*2^(1/2)+1))*(Int(x*KummerM(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2)*exp(-1/2*x^2*(I*2^(1/2)-1)),x)*KummerU(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2)-Int(x*KummerU(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2)*exp(-1/2*x^2*(I*2^(1/2)-1)),x)*KummerM(3/4+1/8*I*2^(1/2),3/2,I*2^(1/2)*x^2))/y(x)]

Attempting computing related first integrals...

Error, (in factor) too many levels of recursion

Download dsolve_factor_dec_24_2024.mw

tracelast; gives long output with this at end

#(IntegrationTools:-Indefinite:-Polynomial,14): return poly/primitivepart*thisproc(primitivepart,var)
 IntegrationTools:-Indefinite:-Polynomial called with arguments: (8*I)*x*KummerM(3/4+((1/8)*I)*2^(1/2), 3/2, I*2^(1/2)*x^2)*x1*2^(1/2)-(3*I)*2^(1/2)*KummerM(3/4+((1/8)*I)*2^(1/2), 3/2, I*2^(1/2)*x^2)*y+(7*I)*2^(1/2)*KummerM(((1/8)*I)*2^(1/2)+7/4, 3/2, I*2^(1/2)*x^2)*y+12*x^2*KummerM(3/4+((1/8)*I)*2^(1/2), 3/2, I*2^(1/2)*x^2)*y+8*x*KummerM(3/4+((1/8)*I)*2^(1/2), 3/2, I*2^(1/2)*x^2)*x1+4*KummerM(((1/8)*I)*2^(1/2)+7/4, 3/2, I*2^(1/2)*x^2)*y, x1, nofactor = false
 #(IntegrationTools:-Indefinite:-Polynomial,8): newpoly := factor(poly)
Error, (in factor) too many levels of recursion
 locals defined as: p = p, primitivepart = primitivepart, base = base, exponent = exponent, subpolys = subpolys, change = change, newpoly = newpoly, u = u

Also, this error can not be cought using try/catch.

bug report: Student:-ODEs:-ODESteps give...

Asked: nm 11353 Product: Maple 2024

December 24 2024

1 1

Maple's Student:-ODEs:-ODESteps solves an ode by doing change of variable on the independent variable, but the resulting ode is wrong and final answer is wrong.

Here is one such example

restart;
ode:=diff(diff(y(x),x),x)*sin(x)^2 = 2*y(x);
Student:-ODEs:-ODESteps(ode):

But this result is wrong. First of all, we can not have both x and t in the same ode. This is what dchange gives

ode:=diff(y(x),x$2)*sin(x)^2-2*y(x)=0;
tr:={PDEtools:-Solve(t=ln(x),x)};
simplify(PDEtools:-dchange(tr,ode,[t]))

It looks like Student:-ODEs:-ODESteps is trying to solve sin(x)^2*y'' + 2 y=0 as EULER type ode.

But Euler type ode will look like x^2*y'' +2 y=0

It seems to have confused sin(x)^2 with x^2. This change of variable it used only works for EULER type ode with polynomial coefficient, not trig coefficients.

Maple 2024.2 on Windows 10

clarification on current status of odete...

Asked: nm 11353 Product: Maple 2024

December 16 2024

1 0

These two issues probably came up before, but I can't find where and when searching Maple primes.

So I thought to summarize the issues I see with odetest in one post, in the hope to get clarification on current status on these from the powers who know.

The first issue

The order in which odetest returns the answer. When odetest is called to check the ode and IC, as in

the_status := odetest(sol,[ode,IC])

One would expect the_status to be a list, where the first entry tells if sol verifies the ode, and the second entry tells if sol verifies IC.

i.e. the order is the same as in the input. right? Since ode is first and IC is second in the input list.

But Maple sometimes mixes the order. See example 1 below. This makes it impossible to determine if the solution verifies the ode or IC, when one of the entries in the_status is zero and the other is not, since order can be reversed sometimes.

Second issue:

When the solution is implicit, Maple gives invalid odetest result on the IC, unless one rewrites the solution using (lhs-rhs)(sol)=0.

i.e. move everything to the left side of the equation with RHS zero. This happens sometimes and when the solution is implicit.

I have thought this was fixed in current Maple, but it is not. I remember this came up before, but can't find when and where.

Example 2 below shows an example.

Will these two issues hopefully be fixed in Maple 2025? Sometimes one forgets to rewrite the solution using (lhs-rhs)(sol)=0 and this results in false negative.

Please see worksheet below. ps. I hope forum manager does not delete this question.

>	interface(version);

>	Physics:-Version();

>

libname;

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

>

restart;

>

Example 1: order of status from odetest is not same as order of input

>	ode:=1+xy(x)(1+y(x)^2x)diff(y(x),x) = 0: IC:=y(1) = 0: sol:=x = 1/(3*exp(y(x)^2/2) - y(x)^2 - 2);

x = 1/(3*exp((1/2)*y(x)^2)-y(x)^2-2)

>	#we see that odetest verifies the ode odetest(sol,ode)

>	#but when adding IC, 0 is now in second entry, instead of first

>	odetest(sol,[ode,IC])

>	#SHOULD NOT zero above be in first slot in the list instead of second slot??

>

Example 2. We must write the solution using (lhs-rhs)(sol)=0

>

restart;

>	ode:=1+xy(x)(1+y(x)^2x)diff(y(x),x) = 0: IC:=y(1) = 0: sol:=x = 1/(3*exp(y(x)^2/2) - y(x)^2 - 2);

x = 1/(3*exp((1/2)*y(x)^2)-y(x)^2-2)

>	odetest((lhs-rhs)(sol)=0,[ode,IC])

>	#we see that now it verified both IC and sol

>

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