Link to actual problem [3694] \[ \boxed {\left (x +y\right ) y^{\prime }+\tan \left (y\right )=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_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 &= x +y, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{x +y}\right ] \\ \left [R &= -y+\arctan \left (x +y\right ), S \left (R \right ) &= \frac {\ln \left (1+\left (x +y\right )^{2}\right )}{2}\right ] \\ \end{align*}