Link to actual problem [8099] \[ \boxed {x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x \left (11 x^{2}+5\right ) y^{\prime }+24 y x^{2}=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_method_2"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {1}{\left (x^{2}+1\right )^{2}}\right ] \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {2 x^{2}+1}{\left (x^{2}+1\right )^{2} x^{4}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {\left (x^{2}+1\right )^{2} x^{4} y}{2 x^{2}+1}\right ] \\ \end{align*}