Link to actual problem [10117] \[ \boxed {x y^{2} y^{\prime \prime }=a} \]
type detected by program
{"unknown"}
type detected by Maple
[[_Emden, _Fowler], [_2nd_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^{\frac {1}{3}}}, S \left (R \right ) &= \frac {\ln \left (x \right )}{3}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}