Link to actual problem [3177] \[ \boxed {y+\left (3 y x^{2}-x \right ) y^{\prime }=-x^{2}-2 x} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]
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 {x}{3 x y -1}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {\frac {3 x y^{2}}{2}-y}{x}\right ] \\ \end{align*}