Example 4.17. Find the general solution of the equation

$$
y^{\prime \prime}-4 y^{\prime}+4 y=0
$$
Solution. We form the characteristic equation

$$
r^{2}-4 r+4=0
$$

from which we find $r_{1,2}=2$. The characteristic equation has equal real roots, so according to formula (4), the general solution is written as follows:

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