Link to actual problem [2039] \[ \boxed {2 \,{\mathrm e}^{x}+t \,{\mathrm e}^{x} x^{\prime }=t^{2}} \]
type detected by program
{"exactWithIntegrationFactor", "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 [\underline {\hspace {1.25 ex}}\xi &= \frac {t}{2}, \underline {\hspace {1.25 ex}}\eta &= 1\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 &=\left (-t^{2}+4 \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x} \\ \frac {dS}{dR} &= -\frac {1}{2 R} \\ \end{align*}