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I'm having problems with a D.E. question,

I'm asked to solve the equation:

[tex]\left(1+y^{'2}\right)y=k^{2}[/tex]

where K is a certain positive integer to be determined later.

This more commonly known, as you probably know, as one of the solutions to the Brachistochrone Problem.

I really have no idea where to start. I've experimented with various methods of integration, which create nothing which I recognized as productive.

A gentle prod in the right direction would be much appreciated!

Thanks!

-930R93

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# Brachistochrone Problem

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