Link to actual problem [15489] \[ \boxed {x^{2} y^{\prime \prime }-2 x y^{\prime }+4 \left (x^{4}-1\right ) y=0} \]
type detected by program
{"second_order_bessel_ode"}
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 &= x^{\frac {3}{2}} \operatorname {BesselJ}\left (\frac {5}{4}, x^{2}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{\frac {3}{2}} \operatorname {BesselJ}\left (\frac {5}{4}, x^{2}\right )}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= x^{\frac {3}{2}} \operatorname {BesselY}\left (\frac {5}{4}, x^{2}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{\frac {3}{2}} \operatorname {BesselY}\left (\frac {5}{4}, x^{2}\right )}\right ] \\ \end{align*}