@acer The fact that dsolve is shown to run without error with option arbitraryconstants= subscripted indicates that the OP is using a quite-recent version of Physics updates.

@rockyicer Good job, and thank you. Yes, I had guessed that including equ6 and using your original equ5 would give it enough information to eliminate f0, but I didn't explore that. I'm glad that you did.

A few hints for part a:

1. A square matrix A such that A^k = 0 for some positive integer k is called nilpotent. You should be able to find some useful details about nilpotent matrices by web searching.
2. There's nothing special about 2023 here; any positive integer will do. In other words, if A is nilpotent, then I - A is invertible.
3. Using the distributive property of matrix multiplication, simplify (by hand, not by Maple) 
   (I - A).(I + Sum(A^k, k= 1..2022)). 

@mmcdara Before one proceeds too far along the lines that you suggest (file transfer, etc.), it should be pointed out that Maple has had a built-in Python interpreter since Maple 2018. I know that you use Maple 2015 and may not be aware of this.

See help page ?Python.

@mmcdara Thanks, I voted up for yours also.

I just made a very small modification to my Answer to have Ia1 expressed in terms of Va1 per the OP's request. The modifcation is to subtract Va1 from the Svars. 

What makes you think that they can't be solved by Maple? Don't you think that it's more likely that it's you, not Maple, doing something wrong?

@jediknight Don't despair: I'm sure that it's possible with Maple V. I used it extensively when it was the current version, and I made many plots far more complicated than this. Try this:

semilogplot(
    map(q-> subs(Q= q, a), Qs), wx= 0.2..2,
    thickness= 5, axes= boxed, labels= [w, Gain], title= `Gain(w, Q, m)` 
);

The wx= 0.2..2 is an essential part of the command. The remaining plot options (from thickness to title) can be omitted until we get the basic plot correct. 

@jediknight You've used extra parentheses that weren't in my command. Also, you've changed plots to plot. It's the extra parentheses that are the direct cause of the error shown. They change the numbers of arguments (which the error message erroneously calls "parameters") of the seq from 2 to 1. 

@jediknight Please upload a worksheet (*.mws) showing the code execution from restart to the latest error.

@jediknight Try this:

plots[semilogplot](
    [seq](subs(Q= Qs[k], a), k= 1..nops(Qs)), wx= 0.2..2, thickness= 5,
    axes= boxed, labels= [w, Gain], title= `Gain(w, Q, m)` 
);

@jediknight Sorry about that; I don't have perfect memory of which version syntax enhancements were made.

Change in to =

@jediknight Like this:

plots[semilogplot](
    [seq](subs(Q= q, a), q in Qs), wx= 0.2..2, thickness= 5, axes= boxed,
    labels= [w, Gain], title= `Gain(w, Q, m)` 
);

The seq command is like an inline for-loop.

@jediknight Okay, change this line

Top:= subs(wx= x, Q= q, a);

to

Top:= evalf(subs(wx= x, Q= q, a));

Although what you did will work, it's better to use the evalf at the end of the calculation rather than at the beginning.

@jediknight Let G be the gain function, which you want to maximize with respect to wx. Let G'(wx) be its derivative. You are doing this, essentially:

1. Let wx_max be the unique positive solution to G'(wx) = 0.
2. Let Top_of_Q be G(wx_max).
3. Let wx_max be the unique positive solution to G(wx) = Top_of_Q.

Step 3 is redundant; wx_max is already known from step 1. The equation G'(wx) = 0 is easier to solve numerically than G(wx) = Top_of_Q, and fsolve will refuse to solve an equation if it can't guarantee the accuracy of the solution to 10 decimal places.

The code that I just gave you doesn't do step 3.

@mmcdara Thanks. The algcurves package I think predates my first Maple version, Maple V r4. Some of the highlighted points are where the tangent is horizontal or vertical; I don't know what the others are. The command plot_real_curve only works for polynomials in two variables, but I like it because it figures out the ranges for the variables automatically.