Link to actual problem [13439] \[ \boxed {y^{\prime }-\frac {3 y}{x +1}+y^{2}=0} \]
type detected by program
{"riccati", "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 {\left (\frac {1}{4}+\frac {x}{4}\right ) \ln \left (x y+y-4\right )}{1+x}-\frac {\ln \left (y\right )}{4}\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 {y^{2}}{\left (1+x \right )^{3}} \\ \frac {dS}{dR} &= -\left (1+R \right )^{3} \\ \end{align*}