Link to actual problem [9102] \[ \boxed {y^{\prime }-\frac {y \left (y+1\right )}{x \left (-y-1+y x \right )}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]
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 &=\frac {x^{2} y^{3}+x^{2} y^{2}}{x^{2} y -x y -x} \\ \frac {dS}{dR} &= 0 \\ \end{align*}