Link to actual problem [4790] \[ \boxed {y^{\prime }-{\mathrm e}^{-x} y^{2}-y=-{\mathrm e}^{x}} \]
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Riccati]
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 &=-y^{2} {\mathrm e}^{-x}+{\mathrm e}^{x} \\ \frac {dS}{dR} &= -1 \\ \end{align*}