Link to actual problem [8441] \[ \boxed {x y^{\prime }+a y^{2} x +2 y=-b x} \]
type detected by program
{"riccati"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Riccati]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x^{2} a}\right ] \\ \left [R &= y+\frac {1}{a x}, S \left (R \right ) &= x\right ] \\ \end{align*}