Link to actual problem [11493] \[ \boxed {t^{2} x^{\prime \prime }-3 x^{\prime } t +3 x=4 t^{7}} \]
type detected by program
{"kovacic", "second_order_euler_ode", "second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_method_2", "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*} \\ \left [R &= t, S \left (R \right ) &= \frac {x}{t}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {x}{t^{3}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {x}{t^{7}}, S \left (R \right ) &= \ln \left (t \right )\right ] \\ \end{align*}