@Jaqr I, as many others, use Maple under Linux with no problems at all, so I don't think that what you have encountered is a Maple issue.  I suspect a corrupted Linux installation. I would suggest that you reformat the partition and reinstall Linux.

Probably the book says something about the complex variable method.  Why not just do what it says?

You don't want to pass someone else's work to your teacher as your own, do you?

Show what you have done to solve that homework problem.  Ask for help if your Maple code runs into problems.

I agree with mmcdara here.  This looks like a problem related to cylindrical or spherical coordinates.  Before you begin making arbitrary changes, it would be good if you explained the context in which this problem arises.

@robertocooper I have only 2020 and 2018, so I cannot compare with the other versions.

@nm Sure, compare the two figures produced in Maple 2018 and 2020 in figs.zip.  Their qualities are not distinguishable but one file is about six times larger than the other.  Something is badly wrong with Maple 2020's EPS export.  This has been noted in other threads within the last year.

I am keeping Maple 2018 for now just for its better EPS exporting capability.

It's difficult to diagnose the issue without seeing your worksheet.  Upload it.

To upload a worksheet, edit your original message, and note the big fat green up-arrow in the toolbar of the panel in which you edit the message.  Click on the arrow to upload.

The question that comes to mind is, what do you expect to see as the graph of the delta function?  Or worse, what would the graph of the derivative of the delta function look like?

@vv The OP is specifically looking for a particular traveling wave solution, hence u = u(x - mu*t).

I must add that I prefer doing change of variables directly as you have indicated. What I showed with dchange was intended to point out the bug in the OP's code.

@Panas95 The differential equation x' = 4 * λ * x^4 - x^6 may be rewritten as x' = x^4 * (4 * λ - x^2).  The equation's equilibria are obtained by setting x' = 0.  That occurs when x = 0 or x^2 = 4*λ.  The equilibria corresponding to x=0 appear as the vertical blue line in the diagram.  Those corresponding to x^2 = 4*λ appear as the parabola λ = x^2/4 in the diagram.

@Carl Love Certainly my calculations are good only if the right-hand sides are constants.  Because of that, before posting my answer I considered changing
eq1 := 2*x^2 + 14*y^2 = 7;
to
eq1 := 2*x^2 + 14*y^2 - 7;
but I decided against it since the latter is not literally an "equation".

Your suggestion of (lhs−rhs)(eq) would have  been a good alternative but I didn't think of it.  Thanks for pointing it out.

@Ioannis In the previous code change c=20 to c=200, and then

plots:-implicitplot(EQ, x=0..1, y=-0.5..0.5);

@Ioannis This worksheet adds labels.

Download: paraboloids-with-labels.mw

@tomleslie The original question asks for "barrel" shapes with circular profiles of radius R, consistent with the equation r = a - R*(1 - sin(phi)).  Your construction produces barrels with sinusoid shapes which is not the same thing.  The OP should refer to Kitonum's construction which produces proper circular shapes.

@Ioannis Here are a few issues for you to consider.

1. The picture that you have supplied in your original post does not agree with the functions that you have included there.  Here is the picture that corresponds to your functions:You  need do decide if you want to change to functions to agree with the picture, or to change the picture to agree with the functions.
2. As you have observed, your arrows do not come out correctly. That's because you are plotting one of the arrows as a binormal vector.  But that's not what you want.  The binormal vector pertains to curves, not to surfaces.  The tangent vectors that you are looking for need to be calculated as the derivatives of S1 with respect to eta and phi.
   
   It is perhaps possible to calculate and plot those vectors through the commands available in the Student:-VectorCalculus or Student[MultivariateCalculus] packages but I cannot help you there since I don't use them.  I find it easier to do such things without the Student packages as I have done to plot the mage shown above.  I am not giving its details right now because I cannot tell whether that's what you are looking for.
3. As to: "Also in the picture included the line (φ=const)".  But there is not just one (φ=const) line; there are infinitely many of them.  All the radial lines in the image shown above are (φ=const) lines.