Link to actual problem [13317] \[ \boxed {y y^{\prime }-3 \sqrt {x y^{2}+9 x}=0} \] With initial conditions \begin {align*} [y \left (1\right ) = 4] \end {align*}
type detected by program
{"exactWithIntegrationFactor"}
type detected by Maple
[[_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 &= \frac {2 x}{3}, \underline {\hspace {1.25 ex}}\eta &= y +\frac {9}{y}\right ] \\ \left [R &= \frac {y^{2}+9}{x^{3}}, S \left (R \right ) &= \frac {3 \ln \left (x \right )}{2}\right ] \\ \end{align*}