Example 2. Integrate the equation $y^{\prime \prime}+4 y^{\prime}+4 y=0$.
Solution. The characteristic equation $k^{2}+4 k+4=0$ has equal roots $k_{1}=k_{2}=-2$.

According to formula (10.18), we obtain the general solution of the original differential equation

$$
y=e^{-2 x}\left(C_{1}+C_{2} x\right)
$$