Link to actual problem [1946] \[ \boxed {x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime }=0} \]
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}{2 x^{3}+3 y}\right ] \\ \left [R &= x, S \left (R \right ) &= 2 x^{3} y+\frac {3 y^{2}}{2}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {4 x^{3} y +5 x^{2}+3 y^{2}}{8 x^{3}+12 y}\right ] \\ \\ \end{align*}