Link to actual problem [14536] \[ \boxed {8 y^{\prime \prime }+6 y^{\prime }+y=5 t^{2}} \]
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 {5 t^{2}}{6}-\frac {40}{3}-\frac {y}{6}\right ] \\ \left [R &= -\left (5 t^{2}-60 t -y+280\right ) {\mathrm e}^{\frac {t}{6}}, S \left (R \right ) &= t\right ] \\ \end{align*}