Solution
= Solution
The <characteristic equation> $r^2+5r+4=(r+1)(r+4)=0$ gives the <complementary function> $C_1e^{-x}+C_2e^{-4x}$. Write the forcing as $30e^x+30e^{-x}$. The <method of undetermined coefficients> gives $3e^x$ for the first term. Because $e^{-x}$ already belongs to the <homogeneous solution>, <resonance in a differential equation> requires a trial $Kxe^{-x}$ for the second; substitution gives $3K=30$. Therefore
$$
\boxed{y=C_1e^{-x}+C_2e^{-4x}+3e^x+10xe^{-x}.}
$$