Link to actual problem [9205] \[ \boxed {y^{\prime }-\frac {-30 x^{3} y+12 x^{6}+70 x^{\frac {7}{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x}=0} \]
type detected by program
{"exactByInspection"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]
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}{-5 y +2 x^{3}+10 \sqrt {x}-5}\right ] \\ \left [R &= x, S \left (R \right ) &= -\frac {5 y^{2}}{2}+2 x^{3} y+10 y \sqrt {x}-5 y\right ] \\ \end{align*}