Link to actual problem [9058] \[ \boxed {y^{\prime }+\frac {y^{3}}{\left (-1+y \ln \left (x \right )-y\right ) x}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= -\frac {-1+y \ln \left (x \right )}{y}, S \left (R \right ) &= -\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 {\ln \left (x \right ) y^{3}-2 y^{3}-y^{2}}{-1+y \ln \left (x \right )-y} \\ \frac {dS}{dR} &= 0 \\ \end{align*}