Link to actual problem [9306] \[ \boxed {y^{\prime }-y \left (y^{2}+y \,{\mathrm e}^{x b}+{\mathrm e}^{2 x b}\right ) {\mathrm e}^{-2 x b}=0} \]
type detected by program
{"abelFirstKind", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Abel]
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 {\left (b y \,{\mathrm e}^{2 b x}-{\mathrm e}^{2 b x} y -{\mathrm e}^{b x} y^{2}-y^{3}\right ) {\mathrm e}^{-2 b x}}{b} \\ \frac {dS}{dR} &= -b \\ \end{align*}