Link to actual problem [1984] \[ \boxed {\left (x^{2}+y^{2}-2 y\right ) y^{\prime }=2 x} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
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 {x^{2}+y^{2}}{x^{2}+y^{2}-2 y}\right ] \\ \\ \end{align*}