I don't think so
This doesn't mean we can't solve it - even approximate the solution numerically.
As I sucked in Lebesgue spaces, I assume is smooth, and for the sake of well-posedness,
and a Taylor's expansion sais
I did try to solve this but alas I am having little success.
Note, this is a non-homogenous.
Thus, begin by finding the general solution of,
Note, this is a Bernoulli, equation
---> general solution.
For the particiluar solution for this ode I had trouble. I went threw many different attempt non of them work. So maybe this is no elementary function which satisfies this particular condition.