the special form of Riccati equation \frac{\mathrm{d} y}{\mathrm{d} x} =ax^{m}+by^{2} has been proved that it is solvable if and only if m=0,m=-2,m=4k/(2k+1),m=4k/(2k-1).
the sufficency is obviously.But how to prove it's necessity?