Link to actual problem [7798] \[ \boxed {x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y=0} \]
type detected by program
{"kovacic", "second_order_ode_non_constant_coeff_transformation_on_B"}
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 &= x, S \left (R \right ) &= \frac {y}{1+x}\right ] \\ \end{align*}