Link to actual problem [13972] \[ \boxed {\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second order series method. Ordinary point", "second_order_change_of_variable_on_x_method_2", "second_order_change_of_variable_on_y_method_1", "linear_second_order_ode_solved_by_an_integrating_factor", "second order series method. Taylor series method", "second_order_ode_non_constant_coeff_transformation_on_B"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x -3}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x^{2}-9}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= \frac {x^{2}}{2}-\frac {9}{2}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= \frac {y}{x^{2}-9}, S \left (R \right ) &= -\frac {\ln \left (x +3\right )}{3}+\frac {\ln \left (x -3\right )}{3}\right ] \\ \end{align*}