Link to actual problem [4258] \[ \boxed {{y^{\prime }}^{3}-a x y y^{\prime }+2 y^{2} a=0} \]
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 {x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{3}}, S \left (R \right ) &= 3 \ln \left (x \right )\right ] \\ \end{align*}