Link to actual problem [9123] \[ \boxed {y^{\prime }+\frac {\ln \left (x -1\right )-\coth \left (x +1\right ) x^{2}-2 y \coth \left (x +1\right ) x -\coth \left (x +1\right )-\coth \left (x +1\right ) y^{2}}{\ln \left (x -1\right )}=0} \]
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_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}+1 \\ \frac {dS}{dR} &= \frac {\coth \left (R +1\right )}{\ln \left (R -1\right )} \\ \end{align*}