Link to actual problem [9401] \[ \boxed {y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\sin \left (x \right )^{2} y=0} \]
type detected by program
{"second_order_change_of_variable_on_x_method_1", "second_order_change_of_variable_on_x_method_2"}
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}{\sin \left (\cos \left (x \right )\right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\cos \left (\cos \left (x \right )\right )}\right ] \\ \end{align*}