Link to actual problem [10491] \[ \boxed {y^{\prime } x -\left (y a +b \ln \left (x \right )\right )^{2}=0} \]
type detected by program
{"riccati", "first_order_ode_lie_symmetry_calculated"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Riccati]
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 &= -\frac {a x}{b}, \underline {\hspace {1.25 ex}}\eta &= 1\right ] \\ \left [R &= y+\frac {b \ln \left (x \right )}{a}, S \left (R \right ) &= -\frac {b \ln \left (x \right )}{a}\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 {\ln \left (x \right )^{2} a \,b^{2}+2 \ln \left (x \right ) a^{2} b y +a^{3} y^{2}+b}{b} \\ \frac {dS}{dR} &= \frac {b}{a R} \\ \end{align*}