Link to actual problem [1048] \[ \boxed {-4 \cos \left (x \right ) y+\left (4 y-4 \sin \left (x \right )\right ) y^{\prime }=-4 \sin \left (x \right ) \cos \left (x \right )-\sec \left (x \right )^{2}} \] With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 0\right ] \end {align*}
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}{-4 y +4 \sin \left (x \right )}\right ] \\ \\ \end{align*}