Link to actual problem [14294] \[ \boxed {\sin \left (2 t \right ) y+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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^{3}}{\sqrt {y}+\cos \left (2 t \right )}\right ] \\ \left [R &= t, S \left (R \right ) &= -\frac {2}{3 y^{\frac {3}{2}}}-\frac {\cos \left (2 t \right )}{2 y^{2}}\right ] \\ \end{align*}