Link to actual problem [5425] \[ \boxed {\left (x +1\right ) y^{\prime \prime }-\left (3 x +4\right ) y^{\prime }+3 y=\left (2+3 x \right ) {\mathrm e}^{3 x}} \]
type detected by program
{"kovacic", "second_order_ode_non_constant_coeff_transformation_on_B"}
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 &= 0, \underline {\hspace {1.25 ex}}\eta &= x +\frac {4}{3}\right ] \\ \left [R &= x, S \left (R \right ) &= \frac {y}{x +\frac {4}{3}}\right ] \\ \end{align*}
\begin{align*} \\ \\ \end{align*}