Link to actual problem [5312] \[ \boxed {y^{2}-\left (y x +2 y+y^{3}\right ) y^{\prime }=-2} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {-y^{4}+x \,y^{2}-4 y^{2}+2 x -4}{y^{3}+x y +2 y} \\ \frac {dS}{dR} &= 0 \\ \end{align*}