The second question is easy: if y is a constant, then both y' and y'' are 0 so the equation becomes 0= 0.
Well I have a stab at it that might lead somewhere. But I can't finish it. Perhaps it will give someone an idea.
Do you have initial conditions on this?
Note that and that .
Then
where a is the accumulated integration constant.
My hope was for a Bernoulli equation, but we have that extra constant that seems to screw things up. I can't find a way to proceed from here.
-Dan
Edit: I was hoping that, since y = constant was a solution (leading to a =0 in the above equation) would help, but it leads to a Bernoulli equation where y = constant is not a solution to the Bernoulli, so this doesn't help.