nm

8679 Reputation

19 Badges

11 years, 273 days

MaplePrimes Activity


These are questions asked by nm

I noticed tags on the post  

https://mapleprimes.com/questions/238161-Why-Maple-Gives-Solution-To-Euler-Ode

keep disappearing. 

I added tags "differential equation" and "dsolve" and so on.  

Later on when I visit this site again I found the tags are all gone.

Why does Mapleprimes remove the tags on post?

Or is someone else removing the tags? If so, why? is something wrong with the tags I've added?

This happend twice on this one post. I noticed earlier today the tags were gone, so I added them again. And now I see the same thing. They are all gone.

I found that sometimes Maple gives

               Error, (in Typesetting:-Parse) too many levels of recursion

When using the Latex command on the output of Student:-ODEs:-ODESteps

Below is worksheet showing it works for some and gives error for others. Is there a workaround for this? I'd like to convert the steps to Latex.

This happens in worksheet using either Display->Typesetting level as EXTENDED or STANDARD

restart;

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1722 and is the same as the version installed in this computer, created 2024, April 12, 17:58 hours Pacific Time.`

ode:=diff(y(x),x)=0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

diff(y(x), x) = 0

\begin{array}{ccc}
 & {} & \textrm{Let's solve}
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)=0
\\
 \textrm{•} & {} & \textrm{Highest derivative means the order of the ODE is}1
\\
 {} & {} & \frac{d}{d x}y \! \left(x \right)
\\
 \textrm{•} & {} & \textrm{Integrate both sides with respect to}x  
\\
 {} & {} & \int \left(\frac{d}{d x}y \! \left(x \right)\right)d x =\int 0d x +\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Evaluate integral}
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\\
 \textrm{•} & {} & \textrm{Solve for}y \! \left(x \right)
\\
 {} & {} & y \! \left(x \right)=\mathit{C1}  
\end{array}

ode := diff(y(x), x, x, x ) + 3*diff(y(x), x, x) + 4*diff(y(x), x) + 2*y(x) = 0;
the_output:=Student:-ODEs:-ODESteps(ode,y(x)):
latex(the_output)

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

Error, (in Typesetting:-Parse) too many levels of recursion

 


 

Download latex_error_ODE_steps_maple_2024_april_13_2024.mw

 

update: Reported to Maplesoft support.

 

This second order (Euler type) ode has no solution for the given two initial conditions. but Maple gives solution with one unresolved constant of integration.

ode:=x^2*diff(y(x),x$2)-2*y(x)=0;
ic:=y(0)=4,D(y)(0)=-1;

sol_no_IC:=dsolve(ode)

The IC's are given at x=0 as a trick to see what Maple will do. We see that at x=0 there is division by zero. So no solution exist for these IC's. But see what happens

sol_with_IC:=dsolve([ode,ic])

It seems Maple simply threw away the part of the solution it could not handle due to the x=0 and just returned the rest.

odetest(sol_with_IC,[ode,ic])

The correct answer should have been the NULL solution (i.e. no solution). 

What Am I missing here? Why does Maple do this? Should Maple have returned such a solution?

Maple 2024 on windows 10.

update:

Reported to Maplesoft support.

I do not know if this caused by same crash in Reproducible--Server-Crash-Kernel-Connection-Has-Been-Lost  or not.

Could someone be able to find out? It happens each time the code is run on windows 10. 

 

26028

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715 and is the same as the version installed in this computer, created 2024, April 3, 20:27 hours Pacific Time.`

restart;

10168

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);


Download another_server_crash_on_int_maple_2024_april_4_2024.mw

ps. reported to Maplesoft.

The above is new crash in Maple 2024. Below shows no crash in Maple 2023:

26028

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715. The version installed in this computer is 1672 created 2024, February 7, 18:34 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

restart;

23104

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);

int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

 

 

Download int_on_maple_2023.mw

Update:

Here is a movie showing the crash. It also happens from the command line. All on windows 10.

My ini file has  nothing in it, other than one command which prints the process ID which I had there for over a year now.  This is after restarting Maple fresh and nothing else running other than this one worksheet.

 

Here is movie showing the crash from command line also. On windows 10 pro.

 

 

The ode  diff(y(x), x)^3 = y(x)*sin(x) should have 3 solutions since it is cubic in diff(y(x),x) and the each of the 3 generated ode's has one solution.

ode:=diff(y(x), x)^3 = y(x)*sin(x);
sol:=PDEtools:-Solve(ode,diff(y(x),x));
Vector(map(X->dsolve(X,'explicit'),[sol]))

But In Maple 2024, using Lie option gives 2 solutions only, while default dsolve gives 3 solutions.

In Maple 2023 using Lie option gives 6 solutions for some reason.

So something changed in Lie solver for dsolve.

Btw, in all the above I am discarding the extra y=0 solution as this is trivial solution and should not have been returned any way, but this is not a big issue

Basically, Maple 2024 Lie solver gives now 2 non trivial solutions when there should be 3 non trivial solutions.

Any one could give an idea why this happens? Should not both solvers return same number of non trivial solutions?


 

18364

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1711. The version installed in this computer is 1708 created 2024, March 27, 16:20 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2024\Physics Updates\lib\`

ode:=diff(y(x), x)^3 = y(x)*sin(x)

(diff(y(x), x))^3 = y(x)*sin(x)

Vector([dsolve(ode)])

Vector(4, {(1) = y(x) = 0, (2) = (3/2)*y(x)^(2/3)+Intat(-(y(x)*sin(_a))^(1/3)/y(x)^(1/3), _a = x)+_C1 = 0, (3) = (3/2)*y(x)^(2/3)+Intat((1/2)*(y(x)*sin(_a))^(1/3)*(1+I*sqrt(3))/y(x)^(1/3), _a = x)+_C1 = 0, (4) = (3/2)*y(x)^(2/3)+Intat(-(1/2)*(y(x)*sin(_a))^(1/3)*(I*sqrt(3)-1)/y(x)^(1/3), _a = x)+_C1 = 0})

Vector([dsolve(ode,useInt,'explicit')])

Vector(4, {(1) = y(x) = 0, (2) = y(x) = RootOf(3*_Z^(2/3)+2*(Int(-(_Z*sin(_a))^(1/3)/_Z^(1/3), _a = _b .. x))+2*_C1), (3) = y(x) = RootOf(3*_Z^(2/3)+2*(Int((1/2)*(_Z*sin(_a))^(1/3)*(1+I*sqrt(3))/_Z^(1/3), _a = _b .. x))+2*_C1), (4) = y(x) = RootOf(3*_Z^(2/3)+2*(Int(-(1/2)*(_Z*sin(_a))^(1/3)*(I*sqrt(3)-1)/_Z^(1/3), _a = _b .. x))+2*_C1)})

Vector([dsolve(ode,Lie)])

Vector(3, {(1) = y(x) = 0, (2) = y(x) = -(2/9)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x))*sqrt(6)*sqrt(exp((1/3)*(Int(cot(x), x)))*sin(x)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x)))/(exp((1/3)*(Int(cot(x), x))))^2, (3) = y(x) = (2/9)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x))*sqrt(6)*sqrt(exp((1/3)*(Int(cot(x), x)))*sin(x)*(_C1+Int(exp((1/3)*(Int(cot(x), x))), x)))/(exp((1/3)*(Int(cot(x), x))))^2})

 


 

Download why_one_less_solution_from_Lie.mw

This below is in Maple 2023 showing difference in Lie solutions
 


 

21112

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

ode:=diff(y(x), x)^3 = y(x)*sin(x)

(diff(y(x), x))^3 = y(x)*sin(x)

Vector([dsolve(ode)]);

Vector(4, {(1) = y(x) = 0, (2) = (3/2)*y(x)^(2/3)+Intat(-(y(x)*sin(_a))^(1/3)/y(x)^(1/3), _a = x)+_C1 = 0, (3) = (3/2)*y(x)^(2/3)+Intat((1/2)*(y(x)*sin(_a))^(1/3)*(1+I*sqrt(3))/y(x)^(1/3), _a = x)+_C1 = 0, (4) = (3/2)*y(x)^(2/3)+Intat(-(1/2)*(y(x)*sin(_a))^(1/3)*(I*sqrt(3)-1)/y(x)^(1/3), _a = x)+_C1 = 0})

Vector([dsolve(ode,Lie)])

Vector(7, {(1) = y(x) = 0, (2) = y(x) = -(2/9)*(_C1+Int(sin(x)^(1/3), x))*sqrt(6*sin(x)^(2/3)*(Int(sin(x)^(1/3), x))+6*sin(x)^(2/3)*_C1)/sin(x)^(1/3), (3) = y(x) = (2/9)*(_C1+Int(sin(x)^(1/3), x))*sqrt(6*sin(x)^(2/3)*(Int(sin(x)^(1/3), x))+6*sin(x)^(2/3)*_C1)/sin(x)^(1/3), (4) = y(x) = -(1/9)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(I*sin(x)^(2/3)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (5) = y(x) = (1/9)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(I*sin(x)^(2/3)*((2*I)*_C1-I*(Int(sin(x)^(1/3), x))+sqrt(3)*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (6) = y(x) = -(1/9)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(-I*sin(x)^(2/3)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3), (7) = y(x) = (1/9)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x)))*sqrt(3)*sqrt(-I*sin(x)^(2/3)*(sqrt(3)*(Int(sin(x)^(1/3), x))-(2*I)*_C1+I*(Int(sin(x)^(1/3), x))))/sin(x)^(1/3)})

 


 

Download Lie_solution_maple_2023.mw

1 2 3 4 5 6 7 Last Page 1 of 165