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Non-linear ODE with pursuit curves

  1. May 21, 2006 #1
    How would one go about finding an analytical solution to the following ODE

    note that we are trying to find y(x) subject to...

    (x*y'')^2 - (1 + (y')^2) = 0
  2. jcsd
  3. May 21, 2006 #2


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    The first thing I notice is that there is no "y" in that equation- just
    y" and y'. If you let u= y' then you have the pair of first order equations
    (x*u')^2- (1+ u^2)= 0 or
    [tex]xu'= \pm\sqrt{1+ u^2}[/tex]
    That gives two relatively simple separable equations.
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