Link to actual problem [8930] \[ \boxed {y^{\prime }-\frac {-2 x^{2}+x +F \left (y+x^{2}-x \right )}{x}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= -\frac {x}{2}, \underline {\hspace {1.25 ex}}\eta &= x^{2}-\frac {1}{2} x\right ] \\ \\ \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 &= -\frac {x}{2} \\ \eta &=x^{2}-\frac {1}{2} x \\ \frac {dS}{dR} &= -\frac {2}{F \left (R \right )} \\ \end{align*}