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?
why riccati equation \frac{\mathrm{d} y}{\mathrm{d} x} =ax^{m}+by^{2} has an elementary functional solution "only" when m=0,m=-2,m=4k/2k+-1
z yuli
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