Link to actual problem [14337] \[ \boxed {\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime }=-2 t} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
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 &= -\frac {t^{2}+1}{2 t +\tan \left (y \right )}, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{t}\right ] \\ \operatorname {FAIL} \\ \end{align*}