Link to actual problem [13455] \[ \boxed {y^{\prime }-4 y+\frac {16 \,{\mathrm e}^{4 x}}{y^{2}}=0} \]
type detected by program
{"bernoulli", "exactWithIntegrationFactor", "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*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= \frac {4 y}{3}\right ] \\ \left [R &= y \,{\mathrm e}^{-\frac {4 x}{3}}, S \left (R \right ) &= x\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 &=\frac {{\mathrm e}^{12 x}}{y^{2}} \\ \frac {dS}{dR} &= -16 \,{\mathrm e}^{-8 R} \\ \end{align*}