Points P, Q, and R lie on the lines through BC, AC, and AB, respectively. Then there's a solution ;-).

@ZnMnCr 

... Some tips:
A good and practical introduction can be found in: Istvan Szabo, Introduction to Engineering Mechanics, starting on page 204, and Repertory and Exercise Book of Engineering Mechanics, starting on page 34. These books demonstrate problems like yours using conventional simplified structural models.
In simplified models, cable elongation is neglected. Simple equations then quickly lead to the solution of corresponding equations for smaller systems. However, if, for example, the guying of a 300-meter-high radio mast is to be calculated as a spatial system under combinations of external loads, then, in my experience, only numerical FEM methods are used, taking into account the large cable mass, sag, and cable elongation. There is powerful specialized software for this. In Maple, in my opinion, it would be worthwhile for you to calculate stresses and support forces in planar cable structures under simplified conditions according to the above-mentioned literature.

@dharr 

... that's exactly what interested me. One of the "strengths" of Zeta/polylog becomes clearly visible. Unfortunately, I'm still too clumsy to plot properly. Instead, I used derive like I did in the old days.

@nm 

... I would like to request an evaluation/transformation of your results with the restriction 0=a<b<2.14. With my limited Maple knowledge, I can't do this, so I'm asking for help. So, I'm not interested in the individual numerical calculations in tabular form.

@nm chini_dgl_a.mw

Happy Easter!

@Alfred_F 

This "unsolvable" equation has a numerical solution for the initial value (1;-1) in the interval [1; 2.700592...]. After a long calculation, I was unable to find a symbolic solution.

@Ronan 

How can point coordinates of the curve be directly retrieved in the plot of the function curve without tabulating (getdata)?

@Ronan 

I didn't know the command "rhs" yet.

@nm 

...exists, but not for every arbitrary initial value. A special solution exists for (sqrt(3);1). There is also another initial value (an incredibly long term).

Quote:

"...For this Abel ode   y'=x+y^3, which is known not to be solvable, Maple hangs on ..."

So the existence and uniqueness theorems of Peano, Picard, and Lindelöf do not apply to this equation if the right-hand side is continuous? But, contrary to the statement in the quote, these very theorems ensure the existence of at least a local solution.

@nm 

Reply to quotes:

"But without using the limit, how else will one find the constants of integration? Are you saying the series must be assumed to have  uniform convergence to use the limit as above?"

Yes.

"I assume Maple also used the limit internally to solve for C2 in this example and give the answer it did. How else could it have found the solution it did otherwise?"

That's probably the case. In such cases, a hint from the software would be helpful.

@nm 

...it should also be noted that uniform convergence of the three summand series must be assumed in the open interval x > 0. Only then can y(t) be assumed to converge uniformly in this interval. And only then is it permissible to calculate y(0) as the sum of the limits of the three summand series.

@nm 

...but that doesn't change the fact that when applying the explicit equation form y = f(t,y), as used in proofs of the existence and uniqueness of solutions, the right-hand side is not continuous/Lipschtz continuous at x = 0. Then Maple's error message should look different, or perhaps a note should appear indicating that a solution was only possible after continuing the solution to the edge of the domain of f(t,y).

Regarding your maple_sol solution, I'd like to know what Maple does with the natural logarithm it contains for x = 0.
The general solution may be correct; I haven't checked it. But classically, no special solution is possible for the initial value at x = 0.

@dharr 

You're right. 2^m is correct instead of 2^(m+1). Thanks for this hint and the tips with the table.

@dharr 

How can coordinates be retrieved from the plot of my "test" file, and how is a table of values ​​created, e.g., from {(m; y) } with y from term (1) from my "test" file for, e.g., m=2...17?