Link to actual problem [9758] \[ \boxed {y^{\prime \prime }-\frac {\cos \left (2 x \right ) y^{\prime }}{\sin \left (2 x \right )}+2 y=0} \]
type detected by program
{"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*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\cos \left (2 x \right )}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \sin \left (2 x \right )^{\frac {3}{2}} \operatorname {hypergeom}\left (\left [\frac {1}{2}, 2\right ], \left [\frac {7}{4}\right ], \sin \left (x \right )^{2}\right )\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\sin \left (2 x \right )^{\frac {3}{2}} \operatorname {hypergeom}\left (\left [\frac {1}{2}, 2\right ], \left [\frac {7}{4}\right ], \sin \left (x \right )^{2}\right )}\right ] \\ \end{align*}