Link to actual problem [6867] \[ \boxed {9 {y^{\prime }}^{2}+3 y^{4} y^{\prime } x +y^{5}=0} \]
type detected by program
{"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 &= -\frac {3 x}{2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= y x^{\frac {2}{3}}, S \left (R \right ) &= -\frac {2 \ln \left (x \right )}{3}\right ] \\ \end{align*}