Nonlinear second order differential equation

[Ioria]

Hello!
It is the first time that i write on this forum. I'm doing a PhD but i can't solve this equation:
it's a non-linear second order differential equation.

ay''+b|y|y'+cy+dx=0

Some ideas?

 

[hunt_mat]

No idea analytically, but have you tried numerically solving it? That way you can get an idea of what it look like and then perhaps asymptotic analysis.

Have you tried writing it as a first order system?