Link to actual problem [8701] \[ \boxed {\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right )=0} \]
type detected by program
{"exactByInspection", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
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}}{y f \left (x^{2}+y^{2}\right )-x}\right ] \\ \left [R &= x, S \left (R \right ) &= \int _{}^{y}\frac {\textit {\_a} f \left (\textit {\_a}^{2}+x^{2}\right )-x}{\textit {\_a}^{2}+x^{2}}d \textit {\_a}\right ] \\ \end{align*}