Link to actual problem [576] \[ \boxed {y^{\prime }-\frac {-1-2 y x}{x^{2}+2 y}=0} \]
type detected by program
{"exact", "differentialType"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
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 {1}{x^{2}+2 y}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {x^{2} y +y^{2}+x}{x^{2}+2 y}\right ] \\ \\ \end{align*}