I need some help, I have this ODE but can't solve it for $y(x)$, I try every method I know, but with no success,please, somebody can help me?



  • $\begingroup$ This equation only has an implict solution: $2\log y + 2\epsilon\log(x + 2 x\epsilon - y^2) - (1+2\epsilon)\log(\epsilon + 2 x\epsilon - y^2) = C$ where $C$ is an integration constant. $\endgroup$ – Winther Nov 17 '14 at 6:43

See here and here. This question is fascinating, where did you find this equation? Is it related to some geometry?

  • $\begingroup$ (your two links are the same.) $\endgroup$ – Calvin Khor May 5 at 19:05
  • $\begingroup$ Sorry, will edit it. $\endgroup$ – Lada Dudnikova May 5 at 19:06


Let $u=y^2$ ,

Then $\dfrac{du}{dx}=2y\dfrac{dy}{dx}$




This belongs to an Abel equation of the second kind.


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