Link to actual problem [9332] \[ \boxed {y^{\prime }-\frac {\left (y-x +\ln \left (1+x \right )\right )^{2}+x}{1+x}=0} \]
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Riccati]
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 &=-\ln \left (1+x \right )^{2}+2 \ln \left (1+x \right ) x -2 y \ln \left (1+x \right )-x^{2}+2 x y -y^{2} \\ \frac {dS}{dR} &= -\frac {1}{1+R} \\ \end{align*}