2

The characteristic equation $r^2 + 6 r + 9 = 0$ has a double root $r = -3$, so the general solution is $y = c_1 \exp(-3 x) + c_2 x \exp(-3 x)$. From the initial conditions we have $y(0) = c_1 = 6$ and (since $y' = (-3 c_1 + c_2) \exp(-3 x) - 3 c_2 x \exp(-3x)$) $y'(0) = -3 c_1 + c_2 = -2$, so $c_2 = 16$. The solution is $y = (6 + 16 x) \exp(-3 x)$.