Link to actual problem [13470] \[ \boxed {x \left (-2 y+1\right )+\left (y-x^{2}\right ) y^{\prime }=0} \]
type detected by program
{"exact", "differentialType"}
type detected by Maple
[_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_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}-y}\right ] \\ \left [R &= x, S \left (R \right ) &= x^{2} y-\frac {y^{2}}{2}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {2 x^{2} y -x^{2}-y^{2}}{2 x^{2}-2 y}\right ] \\ \\ \end{align*}