Example 4. Find the general solution of the equation $y^{\prime \prime}+3 y^{\prime}=0$.
Solution. The characteristic equation $k^{2}+3 k=0$ has roots $k_{1}=0, k_{2}=-3$.

The general solution is given by the formula

$$
y=C_{1}+C_{2} e^{-3 x}
$$