Link to actual problem [14420] \[ \boxed {t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime }=0} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {y}{t^{2}+2 y}\right ] \\ \\ \end{align*}