Link to actual problem [3627] \[ \boxed {y^{\prime } x^{4}+y x^{3}+\csc \left (y x \right )=0} \]
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*} \\ \left [R &= x y, S \left (R \right ) &= -\frac {1}{2 x^{2}}\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 {\csc \left (x y \right )}{x} \\ \frac {dS}{dR} &= \frac {1}{R^{3}} \\ \end{align*}