Link to actual problem [13249] \[ \boxed {y^{2} y^{\prime \prime }=8 x^{2}} \]
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 [\underline {\hspace {1.25 ex}}\xi &= \frac {3 x}{4}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{\frac {4}{3}}}, S \left (R \right ) &= \frac {4 \ln \left (x \right )}{3}\right ] \\ \end{align*}