Link to actual problem [15160] \[ \boxed {\cos \left (x \right ) y+\left (2 y-\sin \left (x \right )\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`], [_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 {y^{2}}{-2 y +\sin \left (x \right )}\right ] \\ \left [R &= x, S \left (R \right ) &= -2 \ln \left (y\right )-\frac {\sin \left (x \right )}{y}\right ] \\ \end{align*}