Preben's suggestion is very good, it points you to the Maple Portal. In addition, there is a more old-fashioned worksheet at ?examples,numeric_DAE which offers further details.

As for your general question, yes, Maple contains all the DAE solvers that MapleSim invokes (plus MEBDFI), both variable step size and fixed step size. For an interesting discussion on various aspects of these solvers, please see here.

f := (a*b+1)*x^3+(a+b+1)*x^2*y^2+(a-b^3)*x*y^2+a*y^10;
# f := collect(f,[x,y]); # unnecessary for this particular f, but often needed for coeffs!    
cl := [coeffs(f,[x,y])]; # adjust as needed, e.g. [x,y,z]
n := numelems(cl); # use nops in old versions
eqns := Equate(cl,[0$n]);
sol := solve(eqns,[a,b]);

There is no solution for this particular f, though, but that was just an example, I presume.

The Lorenz system is available in Maple already. See the Examples section of ?dsolve,numeric,IVP or the startup code of ?MathApps,LorenzAttractor (which is new in Maple 17).
If that doesn't help, please post your code as text or upload your worksheet here.

One way to obtain this (not necessarily the best) is

JLS:=msg->Join([LengthSplit(msg,5)]);

You can certainly wrap that into a printf or sprintf call.

I don't have feedback for the HD 3000/4000 specifically, but Intel chips should work. For general tips, please see our FAQ and the section on updating video drivers in your Install.html.
For officially supported Linux distributions, check our system requirements.

Maple 14 introduced symbolic solutions for BVPs with PDEs, so I recommend that you try to solve the installation problem with Maple 15. The best way is to contact our tech support group at support@maplesoft.com. If you're a customer in Germany / Austria / (German-speaking) Switzerland, you can also contact me at trichard@maplesoft.com.

Then we can see how to formulate the BVP for pdsolve.

On a related note, dsolve's event handling was introduced in Maple 12, just in time for MapleSim 1. Of course, it can also be used without MapleSim. The ?dsolve,numeric,Events page has all the details.

It seems only a numerical solution is feasible. Try this as a starting point for further investigations:

m := 5:
X := diff(F(t),t$2)+(10+8*sin(m*t)/(m*t))*F(t) = 0;
ics := F(0)=1,D(F)(0)=0;
sol_proc := dsolve([X,ics],numeric);
plots:-odeplot(sol_proc,t=0..10);

Just add the conjugate=false option to your LUDecomposition call. This is mentioned in its help docs. You can even omit the simplify call afterwards. But you will need to apply it to C.Transpose(C) to obtain the original Matrix.

@JotaTR I would also replace tan^(-1) with arctan, as the former won't work in 1D input aka Maple notation.
Finally, I'd replace (...)^0.5 with sqrt(...), but that's a matter of taste.

That's probably a misunderstanding. The Linearization template does not require the Control Design Toolbox. You can access the code behind it in MapleSim 5 / Maple 15 by (e.g.)

showstat(MapleSim:-MapleSimTemplate:-Linearization:-LinearizeManual);

[ In MapleSim 6 / Maple 16, that's roughly showstat(MapleSim:-Templates:-Linearization:-Linearize); ]

Can you be more specific about what you entered and what error message(s) you got?

Also, please make sure you installed the latest update 5.02 which can be found here.

Please see the rightmost column (titled "International") in ?2DMathShortcutKeys.
Redefining keyboard bindings is not possible, sorry, but for most (if not all) shortcuts, there are equivalent menu items.
As a last resort, consider migrating from Sweden to a supported country. I'm talking about OS settings and keyboards, of course. ;-)

That's easier to diagnose. See ?LinearAlgebraMigration for help.

If your worksheet still does not run as expected, just upload it here, using the green up-arrow button.

@SamuelTuvare You need to specify in solMine that n2 and n3 are functions of y2 and y3, because the declare statement affects the output only:

solMine:={n2(y2,y3) = -(1/2)*lambda*y2/(mu+lambda), n3(y2,y3) = -(1/2)*lambda*y3/(mu+lambda)};

Then pdetest will return [0,0] as expected.

I'm currently traveling, so I can't test this, but it's worth a try: open the file with one of the FileTools:-Binary commands, then apply StringTools:-Uncompress.