Link to actual problem [8130] \[ \boxed {z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}=0} \]
type detected by program
{"kovacic"}
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 [R &= z, S \left (R \right ) &= \frac {{\mathrm e}^{2 z} y}{z^{2} \left (2 z -1\right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= z, S \left (R \right ) &= \frac {{\mathrm e}^{2 z} y}{z^{2} \left ({\mathrm e}^{2 z}+2 \,\operatorname {expIntegral}_{1}\left (-2 z \right ) z -\operatorname {expIntegral}_{1}\left (-2 z \right )\right )}\right ] \\ \end{align*}