Link to actual problem [8553] \[ \boxed {\left (-x^{2}+y\right ) y^{\prime }=x} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class C`]]
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 {2 x^{2}-2 y +1}{2 x^{2}-2 y}\right ] \\ \left [R &= x, S \left (R \right ) &= y+\frac {\ln \left (-2 x^{2}+2 y-1\right )}{2}\right ] \\ \end{align*}