@Carl Love Indeed weird with that number 10.

I do see that `limit/MrvRight` (called several times) in line 11 has the statement:

 if 10 <= nops(`limit/IndetsRange`(t)) then
        return _Range
 end if;

Whether that has anything to do with the importance of 10 I have no clue so far.

If you replace limit by MultiSeries:-limit you get 1.

restart;
I0:=(x - 11)^(n)*x/(x^(n + 1));                                              
I1:=(x - 11)^(n)/(x^(n));                                                    
is(I1=I0);  
Limit(I0,x=infinity)=MultiSeries:-limit(I0,x=infinity) assuming n::posint;
Limit(I1,x=infinity)=MultiSeries:-limit(I1,x=infinity) assuming n::posint;    
### Carl's example:
MultiSeries:-limit((x-a)^n*x/x^(n+1), x= infinity) assuming n::posint, a>10;
MultiSeries:-limit((x-a)^n*x/x^(n+1), x= infinity) assuming n::posint, a<10;

It has been noticed and mentioned by some (including very knowlegeable people) that the documentation for dsolve/numeric/events is very difficult to follow unless you in fact know all the terms used in advance. There ought to be many more examples to illustrate all the options mentioned.
As it is now you are basically on your own.
To get any help from this forum you need to be very concrete.

For 2015 I get 8.5 MB and for 2017 I get 7.7 MB using Windows 10.

With Maple 2019.2 I get a disastrous result: The program freezes. I have to kill it. The file was created, but had 0 bytes.
I tried 3 times with Maple 2019.2 with the same disastrous result.

I was using the following code in all 3 cases except that the file name test2019 changed.

with(plots);
plotsetup(postscript, plotoutput = `C:/Users/Bruger/test2019.eps`, plotoptions = `color,portrait,height=350,width=350`);
plot3d(x^2+y^2+1, x = -1 .. 1, y = -1 .. 1, axes = boxed, grid = [200, 200]);

Although my patience is not sufficiently large for me to see the message, I think that it is a warning, but not an error. Thus you should in principle have no problem.
I have seen it in other contexts.

@Kitonum The freely available package DirectSearch has the procedure GlobalOptima:
 

DirectSearch:-GlobalOptima(2*x^2 + 2*y^2 + y, {2*x + y <= 6, y^2 - x <= 2},maximize);

It returns: [46.1249999999993, [x = 4.24999999999998, y = -2.49999999999996], 173]

@ecterrab If you apply combine to the integrand Maple quickly gives up:
 

f:=(sin(lambda*x)*cos(mu)+cos(lambda*x)*sin(mu))^k*(x^n)^2;
fc:=combine(f);
int(fc, x);

@djc I use a Danish "speaking" computer bought in Denmark.

(Besides the point here, but that means that [ ] and { } are rather inconveniently placed on the keyboard and require AltGr + 8 for [  and similar for the other. That is a nuissance in Maple.)

@tomleslie I use Windows 10.
I found this:
Windows 10 Home, version 1903, installed 24-07-2019, Build 18362.720.

interface(version);
Standard Worksheet Interface, Maple 2020.0, Windows 10, March 4   2020 Build ID 1455132

@djc I get the same as acer.

kernelopts(version);
   Maple 2020.0, X86 64 WINDOWS, Mar 4 2020, Build ID 1455132

@Abdoulaye Z(0) = 0 determines the value of the parameter C (when a > 0).

The limits (= sup here) of the solutions for x -> infinity can be found for any concrete value of a > 0 and for 0 < a <= 1 it is largest for a = 1. The limit is 3.
I have just modified my worksheet to include this discussion at the bottom.

@BarKop In acer's worksheet I tried adding summarize = true, and it worked:
W := sort(Statistics:-PolynomialFit(3, Rok, TrzbyCelkemEmco, x, svdtolerance=1e-20,summarize=true));

I'm not aware of any restrictions in Maple on the number of equations etc. The limitations are probably determined only by your computer. But how about giving us the equations?

@reza gugheri Try this:
 

restart;

ode:=diff(v(x),x,x)+diff(v(x),x)*cot(x)-v(x)*(cot(x)^2+nu)=a^2*Q(x)/D1;

sol:=dsolve(ode);
indets(sol,specfunc(anything,hypergeom));
?hypergeom

The generalized hypergeometric functions are described in the help.

The ones appearing in sol are found by indets as shown above:

hypergeom( [3/4+1/4*(-4*nu+5)^(1/2), 3/4-1/4*(-4*nu+5)^(1/2)], [1/2], cos(x)^2),
hypergeom( [5/4+1/4*(-4*nu+5)^(1/2), 5/4-1/4*(-4*nu+5)^(1/2)], [3/2], cos(x)^2),
hypergeom( [7/4+1/4*(-4*nu+5)^(1/2), 7/4-1/4*(-4*nu+5)^(1/2)], [3/2], cos(x)^2),
hypergeom( [9/4+1/4*(-4*nu+5)^(1/2), 9/4-1/4*(-4*nu+5)^(1/2)], [5/2], cos(x)^2)

All four are of the form

hypergeom( [n1, n2], [d1], z)

i.e. the first 2 arguments are lists (lenths 2 and 1 respectively). The third argument is cos(x)^2.

@Carl Love Carl, my guess is that suvetha2000 is struggling to understand the code (or has given up).
You always write very neat and compact code, but often it does require some insight to understand it.