Link to actual problem [4256] \[ \boxed {{y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y=0} \]
type detected by program
{"clairaut"}
type detected by Maple
[[_1st_order, _with_linear_symmetries], _Clairaut]
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 &= x +\frac {a}{b}, \underline {\hspace {1.25 ex}}\eta &= \frac {3 y}{2}\right ] \\ \left [R &= \frac {y}{\left (b x +a \right )^{\frac {3}{2}}}, S \left (R \right ) &= \ln \left (b x +a \right )\right ] \\ \end{align*}