Link to actual problem [2077] \[ \boxed {x^{\prime }-x-x^{2} {\mathrm e}^{\theta }=0} \] With initial conditions \begin {align*} [x \left (0\right ) = 2] \end {align*}
type detected by program
{"riccati", "bernoulli", "first_order_ode_lie_symmetry_lookup"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Bernoulli]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\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 &=x^{2} {\mathrm e}^{-\theta } \\ \frac {dS}{dR} &= {\mathrm e}^{2 R} \\ \end{align*}