Link to actual problem [4236] \[ \boxed {4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= \frac {y}{\sqrt {x}}, S \left (R \right ) &= \frac {\ln \left (x \right )}{2}\right ] \\ \end{align*}