Link to actual problem [9002] \[ \boxed {y^{\prime }-\frac {y^{3} {\mathrm e}^{-2 x}}{y \,{\mathrm e}^{-x}+1}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class C`]]
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 {-{\mathrm e}^{-2 x} y^{3}+y^{2} {\mathrm e}^{-x}+y}{y \,{\mathrm e}^{-x}+1} \\ \frac {dS}{dR} &= -1 \\ \end{align*}