Link to actual problem [14315] \[ \boxed {\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 y t +\sin \left (t^{2}\right )\right ) y^{\prime }}{t}=0} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`], [_Abel, `2nd type`, `class B`]]
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 {t}{2 t y +\sin \left (t^{2}\right )}\right ] \\ \left [R &= t, S \left (R \right ) &= \frac {t y^{2}+y \sin \left (t^{2}\right )}{t}\right ] \\ \end{align*}