Link to actual problem [8969] \[ \boxed {y^{\prime }-\frac {x \left (x +2 \sqrt {x^{3}-6 y}\right )}{2}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= -\frac {x^{3}-6 y}{6 x^{4}}, S \left (R \right ) &= -\frac {\ln \left (x \right )}{6}\right ] \\ \end{align*}
My program’s symgen result This shows my program’s found \(\xi ,\eta \) and the corresponding ODE in canonical coordinates \(R,S\).\begin{align*} \xi &= 0 \\ \eta &=6 x^{2} \sqrt {x^{3}-6 y}+4 x^{3}-24 y \\ \frac {dS}{dR} &= 0 \\ \end{align*}