Link to actual problem [956] \[ \boxed {y^{\prime }-y-\frac {\left (x +1\right ) {\mathrm e}^{4 x}}{\left (y+{\mathrm e}^{x}\right )^{2}}=0} \]
type detected by program
{"exactWithIntegrationFactor"}
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 [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= \frac {{\mathrm e}^{3 x}}{\left (y +{\mathrm e}^{x}\right )^{2}}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {{\mathrm e}^{-3 x} \left (y+{\mathrm e}^{x}\right )^{3}}{3}\right ] \\ \end{align*}