Link to actual problem [4044] \[ \boxed {{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y=0} \]
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 [R &= \frac {y}{x^{4}}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}