@onder Sounds strange... I have no such problem in MapleSim 2015 (and neither in 2016 which I used when writing my answer; its Properties pane is the successor to the Inspector/Settings pane).

Did you install the latest update 2015.2(a)? Either via "Help > Check for Updates" or by visiting our downloads page.

If that doesn't help, please contact our technical support team. Make sure to include a screenshot, and list some details like operating system version, and perhaps MapleSim's install logs.

@powerone Practical examples can be found under the MapleSim API documentation. Navigate to the starting point for the help pages by entering ?MapleSim into Maple. The central API command is LinkModel, which returns a module (a Maple data structure) to which you can then apply any API command such as GetEquations, SetParameters, Simulate, etc.

Within MapleSim, you can find pre-defined "templates" for tasks like equation extraction. Or start with the (almost empty) "worksheet" template and add your specific commands.

@od71 The 3D plots towards the end of the paper look as if they were made with Maple. So I would just contact the authors about Maple code.

@Giulianot Yes, I just noticed that later on, after submitting my reply. MaplePrimes scales these bitmaps correctly, unlike some other fora.

Anyways, did you try my suggestions? And how about uploading your worksheet?

@vv It's documented at ?dsolve,system, i.e. unrelated to numerical solvers. For the given system, its side effect is a solution closer to the form we want, particularly without integrals.

In fact, I did not try each and every option, simply because we do not have the TO's full input.

@Giulianot The screenshot is too small for me  to decipher, but I think Maple can reproduce the same solution. You might have to adjust the following code a bit:

sys := {diff(x(t),t) = -k/m*x(t)*sqrt(x(t)^2+y(t)^2), diff(y(t),t) = -k/m*y(t)*sqrt(x(t)^2+y(t)^2)};
ics := {x(0)=x0, y(0)=y0}:
sol := dsolve(sys union ics, {x(t),y(t)}, 'parameters'=[m,k]);
ot := odetest(sol, sys union ics);
numelems([sol]);
sol[1]; # trivial
allvalues(simplify(sol[2],'symbolic'));
allvalues(simplify(sol[3],'symbolic'));

As a side remark, this system has a very simple power series representation, as you can see from

srsol := dsolve(sys union ics, {x(t),y(t)}, 'series', 'order'=10);

So the solutions are

x(t) = sum((-k/m*x0*sqrt(x0^2+y0^2)*t)^j,j=0..infinity);
y(t) = sum((-k/m*y0*sqrt(x0^2+y0^2)*t)^j,j=0..infinity);

if I'm not mistaken.

@ThU Furthermore, the mod syntax has to be corrected:

if i mod 2 = 0 then ...

Alternatively, but less elegant:

if `mod`(i,2) = 0 then ...

@Bendesarts I don't think the system is solvable for those unknowns you listed. In case I have any idea, I will get back to this.

Regarding Worksheet mode vs Document mode, that has been discussed many times on MaplePrimes. Brief instructions for setting the default mode are found in our FAQs.

eqsys := [seq(eq[k],k=1..7)]:
names := indets(eqsys,'name');
numelems(names);

So there are 17 names (variables and parameters) in your system of 7 equations, so you will have to specify which ones you consider as variables to be solved for. Then we can see further.

Apart from that, I would use Worksheet mode for such applications, but that is a matter of preferences.

@Preben Alsholm You're right. I had used expand in my verify call yesterday - probably a copy&paste error of mine.
Sorry for the noise. No side effect with add-on packages or initialization file.

@acer Thanks, that's a good combination. I was just trying to give a hint on InertFrom:-Display before leaving the office for the weekend. No time left for working out any details.

I fixed a couple of typos (besselj should be BesselJ, etc), and cosmetic issues. And the inequality should probably read

Generally check your usage of indexing.
Please see my uploaded file as a starting point for further debugging: Kr_fix.mw

No time left today, sorry. :-)

@Markiyan Hirnyk There is no need to "programmatically confirm the existence of this command". Carl's answer was fully sufficient.

@Preben Alsholm Nice solution, as always! And adding some interactivity is easy:

Explore(odeplot(psol(nn), [x(t),y(t)], t=0 .. 6.7), parameters=[nn=1500..9000]);

@Carl Love In technical support (part of my daily work) the situation is just the other way around. Lost kernel connections in running calculations are reported rarely.
The other ones were a wide-spread issue a few years ago, but have almost disappeared. I don't know if that's because of improvements in Maple or in the OSes.

But let's wait and see what the OP means by "may program begin"...