Solution
= Solution
A quadratic <polynomial> is sufficient: set $y_p=Ax^2$. Its fifth <derivative> vanishes, so $y_p^{(5)}-y_p'=-2Ax$. Matching the forcing gives $A=-1/2$, hence a <particular integral> is
$$
\boxed{y_p=-\frac{x^2}{2}.}
$$
= Solution
A quadratic <polynomial> is sufficient: set $y_p=Ax^2$. Its fifth <derivative> vanishes, so $y_p^{(5)}-y_p'=-2Ax$. Matching the forcing gives $A=-1/2$, hence a <particular integral> is
$$
\boxed{y_p=-\frac{x^2}{2}.}
$$