$($a$)$ Solve the initial value problem

$\frac{dy}{dx}+P(x)y=4x,y(0)=3$

where

$P(x)=\{\begin{array}{cc}2,& 0x1,\\ -\frac{2}{x},& x>1\end{array}$

Use a graphing utility to graph the continuous function $y(x).$