Link to actual problem [1691] \[ \boxed {\frac {y^{2}}{2}-2 y \,{\mathrm e}^{t}+\left (-{\mathrm e}^{t}+y\right ) y^{\prime }=0} \]
type detected by program
{"exactWithIntegrationFactor", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], [_Abel, `2nd type`, `class A`]]
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 &=\frac {-3 y^{2}+6 y \,{\mathrm e}^{t}}{2 \,{\mathrm e}^{t}-2 y} \\ \frac {dS}{dR} &= -{\frac {1}{3}} \\ \end{align*}