Link to actual problem [7293] \[ \boxed {y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y=0} \]
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], [_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 [R &= x, S \left (R \right ) &= \frac {y}{\csc \left (2 x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {y}{\cos \left (2 x \right ) \csc \left (2 x \right )}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= y, S \left (R \right ) &= \frac {\ln \left (\csc \left (2 x \right )-\cot \left (2 x \right )\right )}{2}\right ] \\ \end{align*}