Link to actual problem [5304] \[ \boxed {\left (2 s-{\mathrm e}^{2 t}\right ) s^{\prime }-2 s \,{\mathrm e}^{2 t}=-2 \cos \left (2 t \right )} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]
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 s +{\mathrm e}^{2 t}}\right ] \\ \\ \end{align*}