Link to actual problem [3863] \[ \boxed {\left (1+y+y x +y^{2}\right ) y^{\prime }+y=-1} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {\left (y +1\right ) \left (x +y \right )}{x y +y^{2}+y +1}\right ] \\ \\ \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 {x y +y^{2}+x +y}{x y +y^{2}+y +1} \\ \frac {dS}{dR} &= 0 \\ \end{align*}