Link to actual problem [15248] \[ \boxed {y^{\prime \prime }-10 y^{\prime }+25 y={\mathrm e}^{5 x}} \]
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}{5}-\frac {2}{25}, \underline {\hspace {1.25 ex}}\eta &= x y\right ] \\ \left [R &= \frac {y \,{\mathrm e}^{-5 x}}{25 x^{2}-20 x +4}, S \left (R \right ) &= 5 \ln \left (-2+5 x \right )\right ] \\ \end{align*}