Link to actual problem [8970] \[ \boxed {y^{\prime }-\left (-\ln \left (y\right )+x^{2}\right ) y=0} \]
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^{2} y}{2}+\frac {\ln \left (y \right ) y}{2}+x y -y \\ \frac {dS}{dR} &= -2 \\ \end{align*}