Please note that there are some * characters missing in eq1 and eq2. Try these inputs instead:

eq1 := 3*(1+sin(alfa1)^3)*(30/tan(alfa1)+60/tan(alfa2)+60/tan(alfa3))/(sin(alfa1)^2*cos(alfa1)*tan(alfa1)) = 3*(1+sin(alfa2)^3)*(30/tan(alfa2)+60/tan(alfa3))/(sin(alfa2)^2*cos(alfa2)*tan(alfa2));
eq2 := 3*(1+sin(alfa1)^3)*(30/tan(alfa1)+60/tan(alfa2)+60/tan(alfa3))/(sin(alfa1)^2*cos(alfa1)*tan(alfa1)) = (90*(1+sin(alfa3)^3))/(sin(alfa3)^2*cos(alfa3)*tan(alfa3));

I hope I didn't miss any further ones. Don't have time for the actual question today, sorry.

That should be doable with LinearAlgebra:-EigenConditionNumbers. For the details, you would have to look up the LAPACK users' guide referenced in the help page. I'm not really familiar with that topic, sorry.

Please see ?MmaTranslator in the docs.
For a simple expression or function call like this, you can conveniently write

convert("MeijerG[{{0, 1/2}, {}}, {{0, 1}, {-1, -1}}, a, 1/2]", FromMma);

Have you tried this?

ArrayTools:-Copy(Array1,Array2); # note that this does not output anything
Array2; # check

Please see ?ArrayTools,Copy for more info (options etc.).

If it's only about displaying 5 digits, just use

interface(displayprecision=5);

or its interactive equivalent "Tools > Options > Precision > Round screen display to NN decimal places".

Please see here. If that's not what you need, just give some more details.

No, the Maple Player reads mw and mwz formats only. For mws, you need a full Maple installation. You can then save them as mw files. There is also a worksheet migration assistant built into it that helps you adapting collections of mws files. And it optionally converts 1D input to 2D.

While it doesn't address this particular wish, you might check out our new Student[Basics] package in Maple 18. Please see here for more details.

This can be configured in the Typesetting Rule Assistant, which can be launched via

View > Typesetting Rules...

or by the command Typesetting:-RuleAssistant();

Check "Always" under "Allow shortcut function definition (e.g. f(x):=x)", then press Done.

Please note that Linux Mint is not an officially supported distribution, but given that it's based on Ubuntu, it should basically work by running the bin file in a shell:

./Maple17LinuxX86_64Installer.bin

If you want to install to a system-wide location (as opposed to your home directory), you will need root privileges:

sudo ./Maple17LinuxX86_64Installer.bin

Further instructions are given in Maple's Install.html, which is also viewable online at http://www.maplesoft.com/support/install/maple17_install.html.

I'm not sure if I interpret your question correctly, but the duration can be set easily. Quoting from the help page ?ImpulseResponsePlot:

The second parameter, duration, specifies the time interval to plot. The impulse response is plotted for time starting at zero to duration. If sys is a discrete system, then the number of discrete intervals in the interval depends on  sys:-sampletime.

where sys is the first argument. If that's not what you need, please explain.

Sorry, I have been unsuccessful with your main question. No idea about the large expression. On my computer, odetest consumes too much memory when trying to verify that Y0 is solving the ODE. However, dsolve finds a solution in terms of HeunG functions and their first derivatives, and odetest confirms that.

Moreover, a plot of f1-f2 over 0<s<1 looks good, apart from some numerical noise towards the interval bounds.

A note on your last comment:

Such conversions can often be accomplished through an ln representation, or exp in case of their inverses, i.e. hyperbolic functions. The algebraic expressions (in s) can be simplified by evala. Let's try:

assume(0<s,s<1);
a:=2*arctanh(sqrt((1-s)/(1+s)));
b:=arccosh(1/s);

# from a to b
la:=convert(a,ln);
combine(la);
evala(%);
convert(%,arccosh);
simplify(%);

# from b to a
lb:=convert(b,ln);
convert(lb,arctanh);
evala(%);
combine(%);

So we're almost there. Many people prefer having no sqrts in the denominator.

I might have time tomorrow to take a look at your main question.

To see the numerical data for the probes, go to Project tab > Stored Results and left-click inside. Then in the Inspector tab, rename the result and export it to a csv or xls file by clicking on the fourth icon.

The error message essentially says it: You will need to run Maple with admin privileges for this Compiler:-Setup() call so that it can modify the configuration file (launch.ini in its bin.X86_64_WINDOWS subdirectory). Likewise, if you want to edit that file directly, you will have to run the editor with admin privileges. See also the hint in our FAQ.