Note that Then substitute I think you'll find that the resulting DE is Bernoulli.
You're welcome. Incidentally, I don't think you'll be able to find a closed-form solution of this DE. That is, you'll still have integrals in your final solution, because there are no known antiderivatives for the integrals you get. That's ok. You still get an explicit solution (all the x's on one side), which is nice.