3.3.20 Reduced or special Riccati ode \(y^{\prime }=ax^{n}+by^{2}\)

This is special case of the general Riccati ode \(y^{\prime }=c_{0}\left ( x\right ) +c_{1}\left ( x\right ) y+c_{2}\left ( x\right ) y^{2}\) where now \(c_{0}\left ( x\right ) =ax^{n}\) and \(c_{2}\left ( x\right ) =b\) where \(a,b,n\) are constants. The reduced Riccati ode do not have \(y\) term in it. Only \(x\) and \(y^{2}\) in the RHS of the ode.