Help me with this
, , .
I tried to solve it, but I got non-elementary integral
I guess, then, the question is why you would expect to get a solution in terms of an elementary integral! That's a very non-linear equation and non-linear differential equations tend to have non-elementary solutions. Something as simple (comparatively) as y"= sin(y) has solutions that can only be written in terms of elliptic integrals.