Link to actual problem [4259] \[ \boxed {{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}=0} \]
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 &= x, \underline {\hspace {1.25 ex}}\eta &= -\frac {3 y}{2}\right ] \\ \left [R &= y x^{\frac {3}{2}}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}