Link to actual problem [9296] \[ \boxed {y^{\prime }-\frac {-4 x \cos \left (x \right )+4 \sin \left (x \right ) x^{2}+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 x y+2 \cos \left (2 x \right ) x^{2}+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 y^{2} x +6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+\cos \left (3 x \right ) x^{3}+15 \cos \left (x \right ) x^{3}-6 \cos \left (2 x \right ) x^{3}-10 x^{3}}{4 x}=0} \]
type detected by program
{"abelFirstKind"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \\ \end{align*}