Link to actual problem [8491] \[ \boxed {\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x=-1} \]
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
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*} \\ \\ \end{align*}
My program’s symgen result This shows my program’s found \(\xi ,\eta \) and the corresponding ODE in canonical coordinates \(R,S\).\begin{align*} \xi &= 0 \\ \eta &=x^{2}-2 x y +y^{2} \\ \frac {dS}{dR} &= -\frac {1}{R^{2}-1} \\ \end{align*}