Link to actual problem [5442]
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}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{2}}{2}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{x}}{y}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-x} y^{2}}{2}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {x \,{\mathrm e}^{x}}{y}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-x} y^{2}}{2 x}\right ] \\ \end{align*}