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Brachistochrone Problem

  1. Feb 9, 2010 #1
    Hello,
    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
     
  2. jcsd
  3. Feb 9, 2010 #2
    Integrate [tex]y'=\sqrt{(k^{2}-y)/y}[/tex]. It is useful to use [tex]y=k^{2}sin^{2}(theta)[/tex] .
     
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