Link to actual problem [2521] \[ \boxed {0=-\frac {y^{\prime \prime }}{y}+\frac {{y^{\prime }}^{2}}{y^{2}}-\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y}+2 a^{2}} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)