Link to actual problem [5313] \[ \boxed {y^{2}-\left (\arctan \left (y\right )-x \right ) y^{\prime }=-1} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(y)]`]]
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 {y^{2} \arctan \left (y \right )-x \,y^{2}-y^{2}+\arctan \left (y \right )-x -1}{\arctan \left (y \right )-x} \\ \frac {dS}{dR} &= 0 \\ \end{align*}