Link to actual problem [2705] \[ \boxed {y^{\prime }-2 x \left (y+x \right )^{2}=-1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Riccati]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= -\frac {1}{x +y}\right ] \\ \end{align*}
\begin{align*} \\ \\ \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 &=-2 x^{4}-4 x^{3} y -2 x^{2} y^{2}-2 x -2 y \\ \frac {dS}{dR} &= 0 \\ \end{align*}