Link to actual problem [2524] \[ \boxed {\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}=0} \]
type detected by program
{"kovacic", "second_order_bessel_ode", "exact linear second order ode", "second_order_integrable_as_is"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
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 &= 1+\frac {4}{x}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {x y}{x +4}\right ] \\ \end{align*}