Link to actual problem [15159] \[ \boxed {\left (x -2 y x -y^{2}\right ) y^{\prime }+y^{2}=0} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\).\begin{align*} \\ \\ \end{align*}
\begin{align*} \\ \left [R &= \frac {y}{\sqrt {x}}, S \left (R \right ) &= -\frac {1}{y}\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 {y^{4}-x \,y^{2}}{2 x y +y^{2}-x} \\ \frac {dS}{dR} &= 0 \\ \end{align*}