For the nonhomogeneous linear equation y''+py'+QY = p (x) e (λ x), when the special solution is set to q (x) e (λ x), there is a result after substitution, which must be written in the book. This can be directly memorized and used as a formula, avoiding repeated derivation of special solutions:

Q''+(2λ+p)Q'+(λ^2+pλ+q)Q=P(x)。

For this problem, p=-5, q=6, P(x)=x, λ=2, Q(X)=x(b0x+b 1), after substitution, there are

2b0+(2×2-5)(2b0x+b 1)=x

This is the last formula you wrote.