1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: ODE - Brachistochrone Problem

  1. May 5, 2010 #1
    y[1+(y')^2] = k

    First solve for dx in terms of y and dy, an then use the substitution y = ksin2(θ) to obtain a parametric form of the solution. The curve turns out to be a cycloid.

    My attempt:

    (y')^2 = k/y-1

    dy/dx = sqrt(k/y-1)

    dx = dy/[sqrt(k/y-1)]

    then substitute y = ksin^2(θ)

    dx = dy/[sqrt(1/sin^2(θ)-1]

    dx = dy/[sqrt(cos^2(θ)/sin^2(θ)]

    dx = dy/cot(θ)

    I don't know where to go from here, but the parametric form of y should equal k(1-cos(θ)).
    Any help would be appreciated.
  2. jcsd
  3. May 5, 2010 #2


    User Avatar
    Homework Helper

    shouldn't you sub in for dy in terms of dθ
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook