Solve the IVP:

$\displaystyle \frac{1}{4}x'(t) + 4x(t) = \frac{t}{2} - \frac{t}{2}\mu(t-10),\,x(0) = 8$

where

$\displaystyle \mu(t-a) = \begin{cases} 0,& \text{if $0\leq t< a$}\\ 1,& \text{if $t \geq a$}\end{cases}$

NOTE: I used $\displaystyle \mu$ because I wasn't sure how to do the capital curly "U" that the book uses. This is called the "unit step function".