Link to actual problem [10960] \[ \boxed {x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x \right ) y^{\prime }-y b=0} \]
type detected by program
{"unknown"}
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*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {\left (-x a \right )^{b} {\mathrm e}^{x a} y}{{\mathrm e}^{x a} \left (-x a \right )^{b}-b \left (\Gamma \left (b \right )-\Gamma \left (b , -x a \right )\right )}\right ] \\ \end{align*}