Link to actual problem [3460] \[ \boxed {x y^{\prime }+y+2 x \sec \left (y x \right )=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(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 {1}{x}, \underline {\hspace {1.25 ex}}\eta &= -\frac {y}{x^{2}}\right ] \\ \left [R &= x y, S \left (R \right ) &= \frac {x^{2}}{2}\right ] \\ \end{align*}