Link to actual problem [14535] \[ \boxed {y^{\prime \prime }+3 y^{\prime }-4 y=-32 t^{2}} \]
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 {32 t^{2}}{3}-\frac {16}{3}+\frac {4 y}{3}\right ] \\ \left [R &= -\left (8 t^{2}+12 t -y+13\right ) {\mathrm e}^{-\frac {4 t}{3}}, S \left (R \right ) &= t\right ] \\ \end{align*}