Link to actual problem [3176] \[ \boxed {y+x \left (y^{2}+\ln \left (x \right )\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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 {1}{y^{2}+\ln \left (x \right )}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{3}}{3}+y \ln \left (x \right )\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 {y^{3}+3 y \ln \left (x \right )}{3 y^{2}+3 \ln \left (x \right )} \\ \frac {dS}{dR} &= 0 \\ \end{align*}