Link to actual problem [7775] \[ \boxed {\left (x^{2}+2 x \right ) y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_method_2", "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}{x^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{1+x}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= \frac {1}{2} x^{2}+x, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= \frac {y}{\left (2+x \right )^{2}}, S \left (R \right ) &= \ln \left (x \right )-\ln \left (2+x \right )\right ] \\ \end{align*}