0
$\begingroup$

For some ODEs, it is difficult to get an explicit solution or prove that there exists no solution for it. For example, I want to do this for the following equation $$y^{3} (y- x y'+ (4-x^2)y'') = c$$ where c is a real constant. I'm teaching myself differential equations and I was applying them to a geometry project. I came up with this equation, but I'm stuck as to how to solve it. It doesn't seem to fit anything that I've come across.

Is there a good text that teaches the nonlinear ordinary differential equations and help me to solve them (perhaps by using level sets) or prove that there exists no solution for them?

Thank you for your help.

  • 0
    see here i think this is good http://www-users.math.umn.edu/~olver/am_/odz.pdf – 2017-02-11
  • 0
    This looks like the non-homogeneous form of [legendre equation](https://en.wikipedia.org/wiki/Legendre_polynomials) – 2017-02-11

0 Answers 0