Link to actual problem [1149] \[ \boxed {x^{2} \left (y^{\prime }+y^{2}\right )-x \left (2+x \right ) y=-x -2} \]
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {\left (x y -1\right ) \left (x y -x -1\right )}{x^{2}}\right ] \\ \\ \end{align*}