Link to actual problem [10102] \[ \boxed {y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}=x a +b} \]
type detected by program
{"unknown"}
type detected by Maple
[[_2nd_order, _with_linear_symmetries]]
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 {b}{a}, \underline {\hspace {1.25 ex}}\eta &= y\right ] \\ \left [R &= \frac {y}{x a +b}, S \left (R \right ) &= \ln \left (x a +b \right )\right ] \\ \end{align*}
\begin{align*} \\ \left [R &= x, S \left (R \right ) &= \frac {\ln \left (\textit {\_y1}^{2} y-x a -b \right )}{\textit {\_y1}^{2}}\right ] \\ \end{align*}