Link to actual problem [9312] \[ \boxed {y^{\prime }-\frac {y^{3}-3 y^{2} x +3 y x^{2}-x^{3}+x}{x}=0} \]
type detected by program
{"abelFirstKind", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational, _Abel]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= -\frac {1}{2 \left (x -y\right )^{2}}\right ] \\ \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^{3}-3 x^{2} y +3 x \,y^{2}-y^{3} \\ \frac {dS}{dR} &= -\frac {1}{R} \\ \end{align*}