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I tried to prove, that ideal rope (see picture in attachment) has a shape of the function ch[x]. I finished with this equation

[tex] [h'(x)]^2-h(x)\cdot h''(x)+1=0 [/tex]

Yes, when you try function h[x]=ch[x], you get 0 on the left side, but I have no clue how to solve this equation (find the solution without knowing the solution). Even Mathematica has some problems, if I set boundary conditions. Could you please write how to solve this DE (providing it isn't too complicated, because I don't know much about solving nonlinear DE)

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# DE for Rope

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