Link to actual problem [13721] \[ \boxed {y^{\prime \prime }-6 y^{\prime }+9 y=10 \,{\mathrm e}^{3 x}} \]
type detected by program
{"kovacic", "second_order_linear_constant_coeff", "linear_second_order_ode_solved_by_an_integrating_factor"}
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 &= \frac {x}{3}-\frac {2}{9}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= \frac {y \,{\mathrm e}^{-3 x}}{9 x^{2}-12 x +4}, S \left (R \right ) &= 3 \ln \left (-2+3 x \right )\right ] \\ \end{align*}