Link to actual problem [12313] \[ \boxed {2 y^{\prime \prime }-3 y^{\prime }+17 y=17 t -1} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 2] \end {align*}
type detected by program
{"second_order_laplace", "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*} \left [\underline {\hspace {1.25 ex}}\xi &= 0, \underline {\hspace {1.25 ex}}\eta &= 1+\frac {17 t}{2}-\frac {17 y}{2}\right ] \\ \left [R &= t, S \left (R \right ) &= -\frac {2 \ln \left (2+17 t -17 y\right )}{17}\right ] \\ \end{align*}
\begin{align*} \left [\underline {\hspace {1.25 ex}}\xi &= 1, \underline {\hspace {1.25 ex}}\eta &= -\frac {17 t}{2}+\frac {17 y}{2}\right ] \\ \left [R &= -\frac {\left (2+17 t -17 y\right ) {\mathrm e}^{-\frac {17 t}{2}}}{17}, S \left (R \right ) &= t\right ] \\ \end{align*}