Link to actual problem [9304] \[ \boxed {y^{\prime }-\frac {\left (x y+1\right )^{3}}{x^{5}}=0} \]
type detected by program
{"abelFirstKind", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], _Abel]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \left [R &= y+\frac {1}{x}, S \left (R \right ) &= -\frac {1}{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 &= 0 \\ \eta &=\frac {-x^{3} y^{3}-3 x^{2} y^{2}+x^{3}-3 x y -1}{x^{3}} \\ \frac {dS}{dR} &= -\frac {1}{R^{2}} \\ \end{align*}