Link to actual problem [9000] \[ \boxed {y^{\prime }-\left (-\ln \left (y\right )+1+x^{2}+x^{3}\right ) y=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
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 {x^{3} y}{3}+\frac {2 x^{2} y}{3}+\frac {\ln \left (y \right ) y}{3}-\frac {4 x y}{3}+y \\ \frac {dS}{dR} &= -3 \\ \end{align*}