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I am currently studying the brachistochrone problem in the Boyce-Di Prima D. E. book. While following their indications on the resolution of the problem for the curve as it passes through the point (x0; y0), i find myself wondering what the constant k really means (physically speaking).

Using the bisection method i was told can find a value for k (replacing values in the function f(θ)=2θ-2"sin" θ+"cos" θ-1) but yet again what does that value represent and how is that a solution to the brach. problem?

I know this sounds a little murky, but that's the state of my understanding...so thanks for any help!

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# Meaning of k in D. E. problem

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