Link to actual problem [10014] \[ \boxed {x^{\frac {n}{1+n}} y^{\prime \prime }-y^{\frac {1+2 n}{1+n}}=0} \]
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 &= x, \underline {\hspace {1.25 ex}}\eta &= -y -\frac {2 y}{n}\right ] \\ \left [R &= y x^{\frac {n +2}{n}}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}