You will find that in the Common Symbols palette, fourth row, fourth column.

In your failed version you attempt to solve three equations for two unknowns.  That's not good.  What you want is to solve your three equations for three unknowns, as in:

solve({I__cm = m*r^2, r*T = I__cm*a/r, g*m - T = m*a}, {T, a, I__cm});

This ought to do it:

p := v -> R*T/(v-b) - a/v^2;
numer(p(v)) = 0;

The result is -R*T*v^2 - a*b + a*v = 0, which quadratic in v.  There is no v^3 term.

A couple of errors:

1. In your equations you have variables named mu and mu[1].  That's bad.  One equation declares mu as a scalar, the other makes it an array.  Hence the confusion.  If you want a subscripted mu₁, write it as mu__1 (note the two underscore characters!) not mu[1].  That will not conflict with the variable named mu.
2. Your equations involve a variable T.  It needs to be assigned a numerical value.

A general adivse:  You have:

dsn := dsolve(eval({eqn1, eqn2, eqn3, eqn4, i(0) = 11437, r(0) = 1077, s(0) = 1770000, t(0) = 1087}), {i(t), r(t), s(t), t(t)}, numeric)

Aren't you interested in seeing the system of equations that you are passing to dsolve() to solve?  In general, you should be.  So define:

sys := eval({eqn1, eqn2, eqn3, eqn4, i(0) = 11437, r(0) = 1077, s(0) = 1770000, t(0) = 1087}), {i(t), r(t), s(t), t(t)};

and then examine sys to make sure that what you are passing to dsolve() is what you really mean, and only then do:

dsolve(sys, numeric);

Let's say you have y = f(x) for some function f.  Then dy / dx = f '(x) is a (trivial) differential equation which has y = f(x) as a solution.  You don't need Maple to tell you that.

For instance, if y = cos (x),  then dy/dx = − sin (x) meets your requirements.

I had noted earlier that it would be possible to solve your system of equations through the method of lines.  Now I have worked out the details.  See if this worksheet makes sense.

Download method-of-lines-and-DAEs.mw

It works if you place h(p) in quotes.  I don't know why.

plot('h(p)', p=-1..1);

Added later:

Doing

showstat(MapleTA:-Builtin:-inverf)

we see that inverf() is defined as:

inverf := proc(z::Range(0,1)) ...

and therefore it accepts only numerical arguments in the range (0,1).  In particular, inverf(p) is not accepted if p is an unassigned symbol.  That's bad.  A better-designed inverf() would have returned inverf(p) (unevaluated) for such a p, and that would have made the quotation marks in the plot() command unnecessary.

In this worksheet I show how to calculate the Christoffel symbols for a two-dimensional manifold, that is, a surface embedded in 3D.

Download christoffel-symbols.mw

If you want your plot to appear in a separate window, do one or the other of the following options;

# plot in a separate window
plotsetup(window);
plot(x^2, x=-1..1);

# plot as a maplet
plotsetup(maplet);
plot(x^2, x=-1..1);

# restore the default (inline) plotting mode
plotsetup(default);
plot(x^2, x=-1..1);

Download mw.mw

Download mw.mw

Let's write a for the length of AD.  The fact that we are given a=4 is not essential.  I will write q for the angle ACD, and x for the length of AB.

Apply the law of sines in the triangle ACD:
eq1 := sin(80) / c = sin(q) / a     # forgive me for using degrees for the argument of sin()

Apply the law of sines in the triangle ACB:
eq2 := sin(80+20) / (c + 4/3*c) = sin(q) / x.

Dividing the respective sides of eq1 and eq2, we obtain:
7/3*sin(80) / sin(100) = x / a.

We note, however, that sin(80) = sin(90-10) = sin(90+10) = sin(100), and therefore the previous equation reduces to

x / a = 7 / 3.

In particular, if a = 4, we get x = 28 / 3.

I have used Maple in nothing but Linux for longer than I can remember and haven't had problems such as those that you have described.  Perhaps your Linux installation is broken?

That said, it is possible to run out of java heap memory if you are doing heavy-duty graphics.  In that case consider specifying a larger java heap on the command line, as in

maple -x -j 65536 &

The default java heap is 512.

PS: My current Linux is Ubuntu 22.04.

I see several issues with your worksheet.

• You have three ordinary (not partial) differential equations in e1, e2, e3.  The command to solve ODEs is dsolve(), not pdsolve().
• It looks like the only unknown in your equations is z2(t).  Therefore each of e1, e2, e3 may be solved independently.  There is no guarantee that the z2(t) produced by one of these equations would agree with the z2(t) produced by the other.  Why are you solving the equations as a system?
• Each of your e1, e2, e3 involves a coefficient _C1.  Naming a symbol with a leading underscore is a bad idea.  Such symbols are reserved for use by Maple.  Your _C1 can potentially conflict with Maple's operation.

There may or may not be a solution, depending on some assumptions which you have not stated.

For instance, if you assume that x1_prime, x2_prime, and u are constants, then a solution exists and can be obtained through

pde1 := x1_prime = diff(H(x1,x2),x1) + u*x1 + x2;
pde2 := x2_prime = x1 + diff(H(x1,x2),x2);
pdsolve({pde1,pde2});