The help for CayleyTableGroup specifies: The single required argument is the Cayley table (or multiplication table): an n by n
 Matrix or Array, m, describing the group with n elements, where the [i, j] entry contains the positive integer k such that the product of the ith and j h group elements is the kth group element.

So this needs to be a matrix of integers.

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I don't get an error message for the plot in Maple 2015, just an empty plot. But eval(S,w=1) gives -1.853089027*10^329399 so your numbers seem to be unreasonably large.

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[Edited based on Carl's comment]. At least for real parameters (where the Matrix is Hermitian), there must be four eigenvectors.Not setting phi=Pi circumvents the OPs error message, and 4 eigenvectors are found, but then substituting phi=Pi leads to an error.

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When legend is a list there need to be multiple curves, but you had one curve with 3 points. One way to do this is:

display(pointplot([28,.6481496576],color=blue),pointplot([28,.648149657615473],color=orange),pointplot([28,.6512873548],color=red),style=point,labels = ["k", "y(k)"], legend = ["10-digit precision", "15-digit precision", "Floating-point iteration"] ,legendstyle = [font = ["HELVETICA", 9], location = right]);
 

Not entirely certain I know what you want, but this may be a start.

[Edit: I changed pi (just a symbol) to Pi (the circle constant thing)]

At the beginning I define i to be sqrt(-1) as you want and D to be a regular variable rather than the differential operator.

Maple gives the answer as a sum over roots of a quartic polynomial. To get a simpler formula, you will need to give values to some variables or parhaps tell Maple their signs (using assuming)

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As well as Joe's corrections, you need to assign to y (y:=1). 
 

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I suspect you want gcdex(x^9-a, b*x^6-c, x); but the answer is 1. You may need to specify the numerical value of more of the coefficients.

Try

T := unapply('fsolve'(m(t, c) = -1, t = 0 .. (1/2)*Pi), c, numeric);

In general use unapply to make functions from expressions earlier in the worksheet. The numeric option means that plot and other functions evaluated with a symbolic value will not throw an error.

So the constant _C3 means another condition is required. Presumably you want the solution to drop off at y=infinity.

pdetest suggests your solution does not solve the pde.
 

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Use := to assign the right-hand side to the left. Some other issues also:

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Try entering in 1D Maple input, e.g. at a > prompt use ctrl-M then `≤`

You will see that `≤` is rendered as less-than-or-equals, as it would be in HTML.

Changes in red.
 

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There is a missing *. The differentiation works in Maple 2017.
 

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