Here is another problem from Mathews and Walker that has given me some trouble.

> 
> **1-18**. Find the general solution of
>  $y^{iv}+ 2y''+y=\cos x$.
> 
> 
> 

*Note: Thanks, everyone, for clearing up the interpretation of $y^{iv}$ as the fourth derivative of $y$ and for the clear solutions. 
I had interpreted $y^{iv}$ as $y^{\sqrt{-1} \ v}$ with $v\in \mathbb{C}$. 
Of course, this is an awful nonlinear DE!*