Link to actual problem [10003] \[ \boxed {9 x^{2} y^{\prime \prime }+a y^{3}+2 y=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= x^{\frac {2}{3}}, \underline {\hspace {1.25 ex}}\eta &= \frac {y}{3 x^{\frac {1}{3}}}\right ] \\ \left [R &= \frac {y}{x^{\frac {1}{3}}}, S \left (R \right ) &= 3 x^{\frac {1}{3}}\right ] \\ \end{align*}