Link to actual problem [14435] \[ \boxed {y^{2}+\left (2 y t -2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = \pi ] \end {align*}
type detected by program
{"exact"}
type detected by Maple
[_exact, [_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 {1}{-2 t y +\sin \left (2 y \right )}\right ] \\ \left [R &= t, S \left (R \right ) &= t y^{2}+\frac {\cos \left (2 y\right )}{2}\right ] \\ \end{align*}