Link to actual problem [3466] \[ \boxed {x y^{\prime }+\tan \left (x +y\right )=-x} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_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*}
My program’s symgen result This shows my program’s found \(\xi ,\eta \) and the corresponding ODE in canonical coordinates \(R,S\).\begin{align*} \xi &= 0 \\ \eta &=-\frac {\tan \left (x \right )+\tan \left (y \right )}{1-\tan \left (x \right ) \tan \left (y \right )} \\ \frac {dS}{dR} &= \frac {-\tan \left (R \right ) R +1}{R} \\ \end{align*}