Link to actual problem [5067] \[ \boxed {x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y=0} \]
type detected by program
{"kovacic", "second_order_bessel_ode", "second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_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*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= {\mathrm e}^{2 i x \sqrt {2}\, \sqrt {\frac {1}{x}}}\right ] \\ \left [R &= x, S \left (R \right ) &= {\mathrm e}^{-2 i x \sqrt {2}\, \sqrt {\frac {1}{x}}} y\right ] \\ \end{align*}