Link to actual problem [12255] \[ \boxed {y^{\prime \prime }+\frac {k x}{y^{4}}=0} \]
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 &= \frac {5 x}{3}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x^{\frac {3}{5}}}, S \left (R \right ) &= \frac {3 \ln \left (x \right )}{5}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}