Answer
$\{e^{-3x}, xe^{-3x}\}$
Work Step by Step
Solve the characteristic equation for the differential equation. $$r^2+6r+9=0$$
Factor and solve for the roots. $$(r+3)^2=0$$ $$r=-3,-3$$
The general equation is equal to $y=C_1e^{-3x}+C_2xe^{-3x}$
Therefore, $\{e^{-3x}, xe^{-3x}\}$ is a basis for the solution space.