Link to actual problem [11601] \[ \boxed {\frac {x}{y^{2}}+\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime }=-x} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_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 &= \frac {y^{2}+1}{y^{2} x}, \underline {\hspace {1.25 ex}}\eta &= 0\right ] \\ \left [R &= y, S \left (R \right ) &= \frac {x^{2} y^{2}}{2+2 y^{2}}\right ] \\ \end{align*}