Link to actual problem [13547] \[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {x}{2}-\frac {1}{2 x} \end {align*}
type detected by program
{"reduction_of_order", "second_order_euler_ode", "second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_method_2", "second_order_change_of_variable_on_y_method_2"}
type detected by Maple
[[_Emden, _Fowler], [_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*} \\ \\ \end{align*}