Link to actual problem [4868] \[ \boxed {-y \sin \left (2 x \right )-\left (\sin \left (x \right )^{2}-2 y\right ) y^{\prime }=-2 x} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_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}{\sin \left (x \right )^{2}-2 y}\right ] \\ \\ \end{align*}