Link to actual problem [2421] \[ \boxed {\left (-2 x +1\right ) y^{\prime \prime }+4 y^{\prime } x -4 y=x^{2}-x} \] 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_y_method_2", "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]]
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*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= x^{2}+\frac {1}{2}-4 y\right ] \\ \left [R &= x, S \left (R \right ) &= -\frac {\ln \left (2 x^{2}-8 y+1\right )}{4}\right ] \\ \end{align*}