Link to actual problem [7176] \[ \boxed {y^{\prime \prime }-x^{3} y=x^{3}} \]
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 &= \sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\sqrt {x}\, \operatorname {BesselI}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right )}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\sqrt {x}\, \operatorname {BesselK}\left (\frac {1}{5}, \frac {2 x^{\frac {5}{2}}}{5}\right )}\right ] \\ \end{align*}