# DE for Rope

1. Jul 4, 2006

### Semo727

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

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

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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• ###### rope.jpg
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Last edited: Jul 4, 2006
2. Jul 6, 2006

### BoTemp

Guess and check is the only guaranteed way of finding a solution to any DE. You might be able to use a series expansion here (guess solution of form h(x) = sum(C_n * x^n) and plug in, but I'm not sure. That method is guaranteed to work for linear equations, non-linear it can get tricky.