Link to actual problem [8918] \[ \boxed {y^{\prime }-\frac {2 a}{y+2 F \left (y^{2}-4 a x \right ) a}=0} \]
type detected by program
{"first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= y^{2}-4 x a, S \left (R \right ) &= \frac {y}{2 a}\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 &= y \\ \eta &=2 a \\ \frac {dS}{dR} &= -\frac {1}{8 a^{2} F \left (R \right )} \\ \end{align*}