Link to actual problem [12047] \[ \boxed {t^{2} y^{\prime \prime }-\left (t^{2}+2 t \right ) y^{\prime }+\left (t +2\right ) y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= t \end {align*}
type detected by program
{"reduction_of_order", "second_order_change_of_variable_on_y_method_1", "second_order_change_of_variable_on_y_method_2"}
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*} \\ \left [R &= t, S \left (R \right ) &= \frac {y}{t}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}