143. Find the general solution of the equation $y^{\prime \prime}-6 y^{\prime}+9 y=0$.
Solution. The characteristic equation $k^{2}-6 k+9=0$ has equal roots: $k_{1}=k_{2}=3$. The particular linearly independent solutions of this equation are the functions $y_{1}=e^{3 x}, y_{2}=x e^{3 x}$, and the general solution is given by

$$
y=C_{1} e^{3 x}+C_{2} x e^{3 x}=\left(C_{1}+C_{2} x\right) e^{3 x}
$$