Link to actual problem [14334] \[ \boxed {y+\left (t^{2} y-t \right ) y^{\prime }=-2 t^{2}} \]
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_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}{t y -1}\right ] \\ \left [R &= t, S \left (R \right ) &= \frac {\frac {t y^{2}}{2}-y}{t}\right ] \\ \end{align*}