Link to actual problem [3986] \[ \boxed {\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y=0} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
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 {y^{2}}{-1+2 x +\ln \left (y \right )}\right ] \\ \left [R &= x, S \left (R \right ) &= -\frac {2 x}{y}-\frac {\ln \left (y\right )}{y}\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 {-4 x y -2 \ln \left (y \right ) y}{-1+2 x +\ln \left (y \right )} \\ \frac {dS}{dR} &= 0 \\ \end{align*}