Link to actual problem [9148] \[ \boxed {y^{\prime }-\frac {y \left (-3 x^{3} y-3+y^{2} x^{7}\right )}{x \left (x^{3} y+1\right )}=0} \]
type detected by program
{"unknown"}
type detected by Maple
[_rational, [_Abel, `2nd type`, `class C`], [_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 {y^{3} x^{6}}{x^{3} y +1}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {-\frac {1}{2 y^{2}}-\frac {x^{3}}{y}}{x^{6}}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {y \left (2 x^{7} y^{2}+2 x^{3} y +1\right )}{2 x^{3} y +2}\right ] \\ \\ \end{align*}