Link to actual problem [10095] \[ \boxed {2 x^{2} y^{\prime \prime } y-x^{2} \left ({y^{\prime }}^{2}+1\right )+y^{2}=0} \]
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 [R &= \frac {y}{x}, S \left (R \right ) &= \ln \left (x \right )\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x \ln \left (x \right )}, S \left (R \right ) &= \ln \left (\ln \left (x \right )\right )\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x \ln \left (x \right )^{2}}, S \left (R \right ) &= -\frac {1}{\ln \left (x \right )}\right ] \\ \end{align*}