Link to actual problem [11856] \[ \boxed {4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y=0} \]
type detected by program
{"kovacic", "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_1", "second_order_change_of_variable_on_y_method_2", "linear_second_order_ode_solved_by_an_integrating_factor"}
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*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= x^{2}, \underline {\hspace {1.25 ex}}\eta &= \frac {3 x y}{2}\right ] \\ \left [R &= \frac {y}{x^{\frac {3}{2}}}, S \left (R \right ) &= -\frac {1}{x}\right ] \\ \end{align*}