Int(1/(sqrt(t^4+1)+t^2), t = 1 .. infinity):
% = value(%);
evalf(%); #check

        0.4799537050 = 0.4799537050

Such a system will have generally 2^18 = 262144 solutions.
E.g. the simple one
{seq(x[k]^2=1,k=1..18)};

has exactly 2^18 solutions (all are real). For a more realistic system each solution will be huge.
So, you have no chance. You can at most use fsolve to find some of them.

solve(convert(eq-K,list));

You should use simply  sol(1);

If you really want such a manipulation, use:

eval('''sol'''(x), [x = X]);
eval(%, X=1);

This is not related to Special Relativity.

solve([2*x=6, y=2], x);
has no solutions because y is seen as a parameter. Only when y=2 a solution exists.
You may see this using

solve([2*x=6, y=2], x, parametric);

Of couse the system can be solved wrt all the variables:
solve([2*x=6, y=2], [x,y]);   # or    solve([2*x=6, y=2]);
      [[x = 3, y = 2]]

 

1. Strangely, for name instead of symbol it works.

3. Workaround:

e:=hypergeom([], [], a)+hypergeom([], [], b):
E:=subs(hypergeom=HG,e):
applyrule(HG(x1::anything, x2::anything, a) = 0, E):
subs(HG=hypergeom,%);

Or, use %hypergeom.

You have overlapping patterns, so both

    true, [x = 2]
    true, [y = 2]

are correct.

For uniqueness use e.g.

typematch({2}, set({x :: odd, y :: even}), 's'); s;

Yes, it seems to be a bug. It should give an error as in:
C:=Matrix(B);
A.C;

You should check whether it is fixed in the development library; see:
https://www.mapleprimes.com/questions/222498-Issues-With-Pdsolve

I have also noticed this issue from a yesterday post.

Download bugdiffint.mw

F := unapply(simplify(int(f, [yip = -infinity .. infinity, xip = -infinity .. infinity, tp = 0 .. t])),  t):
Optimization:-Maximize(F, 0..1/2);

I'll take a polynomial of degree 3 (it is easier to write here):
p(x) = x^3 + a1*x^2 + a2*x + a3.

The polynomial has 3 complex roots x1, x2, x3 which depend continuously on (a1,a2,a3) in C^3.
But this dependence is "global" i.e. the multi-function (a1,a2,a3) |--> {x1,x2,x3} is continuous.
If we want to obtain a continuous selection (as it is called in maths) we must jump from one branch to another.

Now, RootOf(p(x), x) denotes the first root (for evalf)  (see ?RootOf for the order of the roots)
and generally this is not continuous as a function of (a1,a2,a3).

A graphical illustration:

consider the polynomial p(x) = (x-1)*(x-2)*(x-3) + c  for 0 <= c <= 1
and look at its largest real root r(c); so, e.g. r(0)=3. The next animation shows clearly that r() is discontinuous as a function of c.

On the other side, if you have another (continuous) function h(y), there is the possibility that r(h(y)) be continuous [for example this happens here if h(y)>1].