Solution
= Solution
The <characteristic equation> of the homogeneous equation is $(r-1)(r-3)=0$. Thus the <complementary function> is
$$
\boxed{y_c=Ae^x+Be^{3x}}.
$$
A linear trial $y_p=ax+b$ gives $3ax+(3b-4a)=3x$, so $a=1$, $b=4/3$. One <particular integral> is therefore $\boxed{y_p=x+4/3}$.