Link to actual problem [13828] \[ \boxed {y^{\prime \prime }-9 y^{\prime }+14 y=98 x^{2}} \]
type detected by program
{"kovacic", "second_order_linear_constant_coeff"}
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*} \\ \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= -\frac {98 x^{2}}{9}+\frac {14}{9}+\frac {14 y}{9}\right ] \\ \left [R &= -\frac {\left (98 x^{2}+126 x -14 y+67\right ) {\mathrm e}^{-\frac {14 x}{9}}}{14}, S \left (R \right ) &= x\right ] \\ \end{align*}