Link to actual problem [11293] \[ \boxed {y^{\prime \prime }-2 y^{\prime } \tan \left (x \right )-\left (a^{2}+1\right ) y=0} \]
type detected by program
{"kovacic", "second_order_change_of_variable_on_y_method_1"}
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}{\sec \left (x \right ) \sinh \left (x a \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\sec \left (x \right ) \cosh \left (x a \right )}\right ] \\ \end{align*}