Link to actual problem [9970] \[ \boxed {y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}=0} \]
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*} \left [\underline {\hspace {1.25 ex}}\xi &= -\frac {x \left (b +r -1\right )}{a -r +2}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= y x^{\frac {a -r +2}{b +r -1}}, S \left (R \right ) &= -\frac {\left (a -r +2\right ) \ln \left (x \right )}{b +r -1}\right ] \\ \end{align*}