Link to actual problem [9008] \[ \boxed {y^{\prime }+\frac {x^{2}-x -2-2 \sqrt {x^{2}-4 x +4 y}}{2 x +2}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= y+\frac {x^{2}}{4}-x, S \left (R \right ) &= -\frac {\ln \left (-x -1\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 &=\frac {2 x \sqrt {x^{2}-4 x +4 y}+2 \sqrt {x^{2}-4 x +4 y}}{1+x} \\ \frac {dS}{dR} &= \frac {1}{2 R +2} \\ \end{align*}