Chapter 8.1, Problem 4ES

State the order of the differential equation, and confirm that the functions in the given family are solutions.

$\begin{array}{l}\text{(a) 2}\frac{dy}{dx}+y=x-1;y=c{e}^{-x/2}+x-3\\ \text{(b)}y\prime \prime -y=0;y=c_1{e}^t+c_2{e}^{-t}\end{array}$