Link to actual problem [5441]
type detected by program
{"unknown"}
type detected by Maple
[[_3rd_order, _exact, _nonlinear], [_3rd_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 &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{y^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{3}}{3}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {x}{y^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{3}}{3 x}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x^{{1}/{3}}}, S \left (R \right ) &= \frac {\ln \left (x \right )}{3}\right ] \\ \end{align*}