Link to actual problem [5108] \[ \boxed {y+y^{\prime }-y^{4} {\mathrm e}^{x}=0} \]
type detected by program
{}
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*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= -\frac {y}{3}\right ] \\ \left [R &= y \,{\mathrm e}^{\frac {x}{3}}, S \left (R \right ) &= x\right ] \\ \end{align*}