Link to actual problem [14433] \[ \boxed {{\mathrm e}^{y t} y+t \,{\mathrm e}^{y t} y^{\prime }=2 t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 {{\mathrm e}^{-t y}}{t}\right ] \\ \\ \end{align*}