Link to actual problem [9258] \[ \boxed {y^{\prime }-\frac {y^{2}+2 x y+x^{2}+{\mathrm e}^{2 \left (-y+x \right )^{2} \left (y+x \right )^{2}}}{y^{2}+2 x y+x^{2}-{\mathrm e}^{2 \left (-y+x \right )^{2} \left (y+x \right )^{2}}}=0} \]
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*}
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 &= y \\ \eta &=x \\ \frac {dS}{dR} &= \frac {1}{{\mathrm e}^{2 R^{2}}+R} \\ \end{align*}