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First Order, Second Degree ODE

  1. Apr 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve y^2*(1-(dy/dx)^2)=1

    2. Relevant equations



    3. The attempt at a solution

    I expressed the ODE in terms of dy/dx and considered two cases. I got

    (a) y^2 = 1 + (x+C)^2
    (b) y^2 = 1 + (-x+C)^2 where C is a constant

    However, my professor told me that there is another way to do this. He hinted me that this was some well-known ODE. Can someone enlighten me on where to find out more about this ODE? Thank you.
     
  2. jcsd
  3. Apr 5, 2012 #2
    That looks suspiciously like something trigonometric. Perhaps you could do a change of variables y=sin(z) or something similar.
     
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