@nm 

Could you provide a test file? What I see in your video is extreme. I only have these black or clipped windows when I have a Maple session running for a long time with many worksheets open. The clipping is also visible in other applications running in parallel which is an indication that the memory for the graphics adapter (virtual or phsyical?) is running out.

After a logout from Windows everything is back to normal.

Anything special about your graphic adapters?

Yes, I had this before. It happens from time to time and I assume it is related to Java and Windows.

If Crtl,Shift,Enter still executes the worksheet then something hinders the GUI to enable the !!! button.

You could also try to change worksheet tabs to see if that enables the button. This "method" enabled in some instances the interupt button.

@ecterrab 

I have done a punctual check of the new solutions provided by dAlembert. Looks good, but provides less solutions in the real domain.
For me it is not a first choice to solve this initial value problem. odeadvisor still does not list this type. Is it for the reason that other methods are considered superior? Anyway, IVPs leads me to a subtely that I overlooked when speculating about odeadvisor.

odeadvisor advises on ordinary differential equations and not on initial value problems. In this sense, no suggestions on methods are made to solve an IVP. 👍

@dharr 

I have tried on the solution obtained with the dsolve method dAlembert

subs(x=-4,sol);
allvalues(%,implicit = true);

Only one root is obtained for negative x whereas 3 roots are obtained for x beeing positive. To make sure I also set one of the roots not obtained with dAlembert as root selector

RootOf(op(rhs(sol)),-4.725448724):
allvalues(subs(x=-4,%));
evalf(%);

-> -4.721 is not a root.

Looks to me that the RootOf expression obtained with dAlembert is not pointwise equivalent to your implicit solution. It provides less solutions to the ode. All that assuming that RootOf performs as described on the allvalue helppage  (i.e. it provides all roots).

Again 👍👍

@dharr 

Its apparent from your solution that allvalues did not provide all solutions when working symbolically and did also not warn about missing solutions when working numerically. Why allvalues decided to solve numerically in one case is still unclear.

Implicitly your answer sheds light on questions about the results of dsolve depending on solution methods. That is very revealing.

Thanks allot!

Have you forgotten to add an attachement?

@

Very interesting background.

I wonder to what extent such advanced integration methods will one day be available in Maple's standard libraries. Perhaps the need for more PDE functionality and/or performance will trigger this. Some users have asked for it.

Thank you!

@nm 

Or nothing at all, as here if the rhs is <>0

duffing:=m*diff(y(t),t,t) + b*diff(y(t),t) + c1*y(t) + c3*y(t)^3  =  F(t);
DETools[odeadvisor](duffing,y(t));
             /  2      \                                          
             | d       |     / d      \                    3      
duffing := m |---- y(t)| + b |--- y(t)| + c1 y(t) + c3 y(t)  = F(t
             |   2     |     \ dt     /                           
             \ dt      /                                          

  )


                             [NONE]

What irritates me more is the implicit solution, which seems to pass odetest only if the singular solution is taken into account

DETools[dalembertsol](ode):
solve(subs(x=0,y(0)=0,%[1]),{c__1});
sol3:=subs(%,%%[1]);
simplify(odetest(sol3,ode));
subs(sol,%);

Not sure how to interprete this. Is, in this case, this solution for this IVP a valid solution? Can provide dAlembert a solution at all or is it for that reason excluded from the list of methods? This would mean that certain pattern of methods are not possible.

@nm 
This pattern should also give a true. Shouldn't it?

`odeadv/y=_G(x,y')`

@nm

Maple agrees too

DEtools:-odeadvisor(ode,[dAlembert])
                          [_dAlembert]

However, it looks to me that the method [_dAlbembert] does nothing more than this call to DETools (to be confirmed)

DETools[dalembertsol](ode);
solve(subs(x=0,y(0)=0,%[1]),{c__1});
subs(%,%%[1]);
plots:-implicitplot(%)

which does not accept ICs but returns 2 solutions where one of them comes with an integration constant.

No IC are accepted here

DETools[dalembertsol](ode,ic);
Error, (in ODEtools/info) found wrong extra argument(s): y(0) = 0

A call of dsolve with the method [_dAlbembert] should probably do the same or return the implicit solution from above.

We could also ask, why Maple did not list the type dAlembert. Maybe it is done on purpose to suggest/advise most suitable methods.

@Carl Love 

Thank you. The links are helpful. What was not helpful in the context of this question was how I got introduced to the term homogeneous a long time ago.

Maple does not seem to classify the "other" homogeneous cases that Wikipedia mentions in the link above as such and uses different terms. I am referring here to

Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

@Carl Love

For completenes, my refined attempt fits now to homogeneous, Class A ode

simplify(isolate(ode,diff(y(x), x))):
lhs(%)=simplify(eval(rhs~(%), y(x)= x*v)): 
subs(v=y(x)%/x,%);

Could you provide a link to a nonlinear homogeneous definition? I could not find anything useful.

@nm

Thank you for confirming. I could also test it on a 2024.0 installation. The 2024.0 installation shows the output in 2D-Math and in 1D-Math on the first call.

@Ohmyus 

You do forward kinematics where the d[i] are inputs into the system and the platfrom orientation and position are the outputs.

As you have leanred form the other comments, there are no explicit solutions known. If you find one, you can publish it.

As Carl said, you have to solve the problem numerically.

@nm 

I do not have 2024.0 any more. It was uninstalled at the update.

Still no hangs with 30, 40 and 50.

With restart timing was always precise within one second.

500 does not termiante and could not be interputed. Termination of mserver was required.

To give you an idea: This is what my computer offers in terms of speed.

from

https://www.mapleprimes.com/posts/222505-Maple-Performance