Link to actual problem [3727] \[ \boxed {\left (x^{3}+2 y\right ) y^{\prime }-3 x \left (2-y x \right )=0} \]
type detected by program
{"exact", "differentialType"}
type detected by Maple
[_exact, _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^{3}+2 y}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {x^{3} y -3 x^{2}+y^{2}}{x^{3}+2 y}\right ] \\ \\ \end{align*}