Link to actual problem [14634] \[ \boxed {t^{2} \left (-1+\ln \left (t \right )\right ) y^{\prime \prime }-y^{\prime } t +y=-\frac {3 \left (1+\ln \left (t \right )\right )}{4 \sqrt {t}}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = 0] \end {align*}
type detected by program
{"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 {y}{t}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= t, S \left (R \right ) &= \frac {y}{\ln \left (t \right )}\right ] \\ \end{align*}