Link to actual problem [6305] \[ \boxed {y^{\prime \prime }-2 y^{\prime }+5 y=25 x^{2}+12} \]
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 {25 x^{2}}{2}-1+\frac {5 y}{2}\right ] \\ \left [R &= -\left (5 x^{2}+4 x -y+2\right ) {\mathrm e}^{-\frac {5 x}{2}}, S \left (R \right ) &= x\right ] \\ \end{align*}