Link to actual problem [8954] \[ \boxed {y^{\prime }-\frac {y^{2}+2 y x +x^{2}+{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}{y^{2}+2 y x +x^{2}-{\mathrm e}^{2 F \left (-\left (x -y\right ) \left (x +y\right )\right )}}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}