Link to actual problem [6397] \[ \boxed {y^{\prime \prime }+y^{\prime }+y=x^{2}+2 x +2} \] Given that one solution of the ode is \begin {align*} y_1 &= x^{2} \end {align*}
type detected by program
{"reduction_of_order", "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*} \\ \\ \end{align*}