Link to actual problem [9881] \[ \boxed {x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }-a^{4} x^{3} y=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_high_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 [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselI}\left (0, x a \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselJ}\left (0, x a \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselK}\left (0, x a \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\operatorname {BesselY}\left (0, x a \right )}\right ] \\ \end{align*}