Link to actual problem [15036] \[ \boxed {y^{\prime }-\frac {y}{2 \ln \left (y\right ) y+y-x}=0} \]
type detected by program
{"exact", "differentialType", "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 {1}{2 \ln \left (y \right ) y +y -x}\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 {2 y^{2} \ln \left (y \right )-2 x y}{2 \ln \left (y \right ) y +y -x} \\ \frac {dS}{dR} &= 0 \\ \end{align*}