Link to actual problem [15434] \[ \boxed {\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y=\left (x -1\right )^{2} {\mathrm e}^{x}} \] With initial conditions \begin {align*} [y \left (-\infty \right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
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*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}