Link to actual problem [6459] \[ \boxed {y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}}=0} \] With the expansion point for the power series method at \(x = 0\).
type detected by program
{"second_order_change_of_variable_on_y_method_2", "second order series method. Irregular singular point"}
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*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{x}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}