I am currently dealing with the following ODE as a stationary, special case version of a PDE model derived from Kuramoto-Sivashinsky.
$$y'' y' = ay$$
Where $a$ is a real (constant) parameter.
I am going through different handbooks (even asked chatgpt haha) to try and classify this equation or even (best case scenario) find some insight on analytical solutions/solution properties. However, this search has not provided much yet and I'm currently working on the linearization.
Has anyone here stumbled across a similar ODE before? Any help would be greatly appreciated!