Link to actual problem [3195] \[ \boxed {y^{2}+\left (-y+{\mathrm e}^{x}\right ) y^{\prime }=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class A`]]
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 {y \,{\mathrm e}^{x}}{-y +{\mathrm e}^{x}} \\ \frac {dS}{dR} &= 0 \\ \end{align*}