Link to actual problem [10820] \[ \boxed {\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y=-k \,x^{m}-b} \]
type detected by program
{"exact"}
type detected by Maple
[_exact, _rational, [_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}{y +A \,x^{n}+a}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y^{2}}{2}+A \,x^{n} y+a y\right ] \\ \end{align*}