Link to actual problem [3481] \[ \boxed {\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}=0} \]
type detected by program
{"bernoulli", "first_order_ode_lie_symmetry_lookup"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)\begin{align*} \\ \left [R &= x, S \left (R \right ) &= -\frac {1}{2 \left (1+x \right )^{2} y^{2}}\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= -\ln \left (y\right )+\frac {\ln \left (x^{4} y^{2}+4 x^{3} y^{2}-4 x^{2} y^{2}-16 x y^{2}-9 y^{2}-1\right )}{2}\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 (1+x \right )^{2} y^{3} \\ \frac {dS}{dR} &= -1-R \\ \end{align*}